In the 31st Century at the planet Troy, the space explorer Ulysses prepares to take his ship, the Odyssey, and its crew back to Earth, where political unrest between impatient Princes threatens the peace. Ulysses must also return to the Earth before the next comet travels across the sky there, otherwise his wife Penelope's duty will be to find another husband. Before their journey begins, the Odyssey's crew celebrates Ulysses' son Telemachus' birthday, and he is given a new little robot named Nono. On the Odyssey's journey back to the Earth, the Odyssey's computer Sherka detects a previously unknown planet. As the planet's location is logged on file, a white light emanates from the planet and abducts Telemachus. He is taken prisoner and comes across two other children from the planet Zotra (also known as the White Planet), Yumi and her brother Numinor. He tells Telemachus that they are all prisoners of the disciples of the Cyclops. The Cyclops steals energy from children and gives it t

The Odyssey comes across a lifeless city world. On hearing that its people had the technology to bring the dead back to life, Yumi takes Numinor to the planet to revive him. However, she learns why there is no life in the city.

On an isolated asteroid, the blind Heratos and his Zotrian companion Atena attempt to contact the Odyssey. The gods of Olympus, who took Heratos' sight, offer to return it if he sends Ulysses to the graveyard of wrecks and hulks. After they threaten Atena, he agrees to betray Ulysses. The Odyssey receives their signal and heads towards Atena and Heratos' asteroid. Atena explains how she was found abandoned as a child in a spaceship by Heratos, and Heratos himself tells Ulysses of a black sphere that lay next to Atena in the ship. After touching the sphere, he found it to be a ship's log showing a map of Olympus and the route through the galactic glaciers. To prevent him from knowing too much, the gods took away his sight, and he and Atena ended up stranded on an asteroid. Heratos pretends give Ulysses directions to the galactic glaciers, but they are instead directions to the graveyard of wrecks and hulks. After confessing his crime to Atena, they both travel into space after Ulysses.

Ulysses is saved from a Trident attack by Chronos, the god of time, who wants to use him as leverage to be allowed to reenter the home of the gods.

The ship passes a moon that brings Numinor back to life, since it's from his home planet of Zotra. When they investigate, the children disappear and Numinor suspects they've been kidnapped by a legendary witch.

Aeolus, King of the winds, kidnaps Ulysses to provide entertainment for his daughter's birthday party. Unable to watch her father's cruel sport, she frees the captives and helps them escape.

Ulysses encounters Sisyphus, a king condemned to fill a crater with boulders for all eternity for having dared to want the secret of immortality. Zeus has promised Sisyphus he can leave if he makes Ulysses take his place.

A space storm revives the companions as crazed automatons who take over the ship and try to crash it into space glaciers.

Passing through the domain of the great Sphinx, Ulysses must answer his riddle to leave safely. His treacherous daughter kidnaps the children and plots to make Ulysses her slave.

The Odyssey comes across a planet ruled by the evil Antipodes, who keeps a menagerie of miniaturized pets. Antipodes detects and shrinks down the Odyssey using his powerful prism, and the ship crashes down into the sea, close to his island. Ulysses undertakes a little reconnaissance using one of the shuttles, but ends up being trapped in an oyster and encased in a pearl. Losing track of Ulysses, Telemachus takes another shuttle to his father's last known location and encounters lots of other miniaturized shipwrecks on the seabed. Telemachus' shuttle is scooped up, along with the shipwrecks by fishermen working for Antipodes. The pearl containing Ulysses is taken to Antipodes, and Ulysses manages to get his shuttle free. Discovering how to use the crystal to return themselves to normal size, Ulysses and Telemachus avoid Antipodes and his cat and manage to shrink him down as well as restoring themselves. They take the prism with them and enlarge the Odyssey back to its original size, whi

Trying to help a stranded astronaut, Ulysses tries to find a hidden base on one of the deadly twin planets Scylla or Charybdis.

Ulysses follows a Trident carrier in hopes of learning more about the way out of Olympus, and finds himself trapped in bizarre worlds. To save the children, he will have to give up his memories.

Pirates kidnap the children to force Ulysses and No-No to brave the danger of the Sirens, said to guard a map of the Olympus universe.

Coming across a piece of Zotra that could bring Numinor back to life, Ulysses and Yumi pursue it to a swamp planet where they are ambushed by monsters who can copy their forms.

Exploring a planet remarkably similar to the Earth of 200 million years ago, with the continents different from the present, Ulysses and the children quickly come under attack by giant mutant vultures. Forced to land, they seek refuge in a cave and discover an advanced underground city. There, they come across a strange group of large egg-shaped structures, while Sherka warns Ulysses that there are about to be immense seismic disturbances on the planet. Counting nine eggs, one for each planet in Earth's solar system, Ulysses opens the third egg, representing Earth. A winged woman named Sauria emerges and tells Ulysses that they are on Earth and that her people were all put in suspended animation to protect themselves from a huge flood covering the Earth, when the gods lived on Earth and her people were their slaves. The gods left without them, and used the mutants vultures named Keconopters to protect their spaceships before they left. In secret, Sauria's people built the Ark, containi

Near the zone of the Kingdom of Hades, Ulysses and the children are rendered unconscious, and the Odyssey is taken into another dimension. Their companions are taken from their chamber and placed on the Odyssey's bridge. An Earth-like planet is detected, and the now-awakened Ulysses uses a shuttle to investigate. As he does so, his companions are manipulated into piloting the Odyssey to the planet, known as Aim, by Circe the enchantress. She turns the Odyssey's crew into swine so as to be her slaves. Ulysses encounters a space commander named Hermes who tells him that his crew were taken by Circe, who wants to build a giant tower of knowledge. When she has all the knowledge of the universe, she will be able to stand up to the gods. Hermes shows Ulysses how to get to the tower, and once there he and Nono encounter Circe's librarian, also named Hermes. Ulysses finally finds Circe, who refuses to return Ulysses companions to normal. When she finds out who he is, she tells him that he can

The shapechanger Nereus calls Ulysses for help when Shark Men, servants of the gods, take over his planet.

Princess Ariadne comes upon the Odyssey, and asks for Ulysses' help in saving her lover Theseus, who has been exiled to her father's labyrinth to be killed by the fearsome Minotaur.

Mercurius, the bubble-dwelling "grandson of the gods," enlists Ulysses' help in taking a jewel from the brow of the giant Atlas under the promise that it will give him the power to send Ulysses home.

The Odyssey comes under attack by Tridents as Telemachus is piloting a shuttlecraft. Telemachus spots a planet with a giant hole in its side, and Ulysses takes the Odyssey into the planet's hole to protect it from the Tridents. As they enter the hole, they notice that the Tridents are unable to follow them, exploding when they try. Soon, all the damage incurred by the Odyssey repairs itself, and a voice introducing himself as the Magician in Black tells them that he was responsible. Ulysses and the children are transported to his palace, and there they meet the Magician, who tells them that he is more powerful than the gods. To prove it, Ulysses asks him to free his companions. The Magician agrees, for an undisclosed price, and soon they are reunited with their revived friends. Later, the Magician holds a feast for Ulysses and his companions. Numinor notices that his servants are also Zotrians, and the Magician explains to Ulysses that they are his slaves. The Magician then reminds Uly

Passing a ringed planet that looks just like Saturn, the Odyssey receives distress signals from a disabled ship. Ulysses and the children rescue the pilot, and she tells them her name Hypsipyle is and she wishes to go to the base at Istria. She wants help in freeing the women of Lemnos, after all the men imprisoned them since they rebelled against their male masters. On Lemnos, it is the women who do all the work, and work in the factories producing Tridents for the Sharkmen. As punishment for her disobedience, the Lemnos Council of Four imprisoned Hypsipyle's father, the king of Lemnos. As Ulysses escorts Hypsipyle to Istria, she tells him that her father may know the location of the Kingdom of Hades. At Istria, they find the entire base has been destroyed by Tridents, so they then head off to Lemnos itself. There, they find the factories empty, with all the women still imprisoned. They free the women, but on board the Odyssey Yumi senses that they are in danger, and so she and Telema

The Odyssey is drawn off course by an unknown force, and after Ulysses attempts to fly the ship by manual control, Sherka informs him that machines only obey machines. Ulysses and the children are strapped to their seats by Sherka while she continues to obey the unknown controller. Soon, a voice introduces himself as Cortex, chief of the Planet of Machines, and tells them that he wants to keep the Odyssey. Once on the planet, the robot inhabitants begin stripping the Odyssey of its robotic components, including Nono, who catches the attention of a golden female counterpart of his named Nanette. She wants to take him to Cortex, while Ulysses and the children are also removed from the Odyssey. Nanette tells Nono that her people must keep Cortex running otherwise the consequences will be terrible. She tells Nono to forget his human friends, who are kept as exhibits for the machines to look at. Nono rescues Ulysses and the children, and Nanette tells them that Cortex will punish them. Ulys

Ulysses and the children are sent back in time and meet the original Ulysses, Telemachus and Penelope of Homer's epic.

Needing raw materials to repair the Odyssey, Ulysses travels to a world where the inhabitants are addicted to eating seeds which induce amnesia.

The Odyssey responds to a distress call from Queen Calypso, who tells him that if he saves her planet she will tell him the way back to earth. Calypso has been ordered by Zeus to betray Ulysses, but she falls in love with him and cannot carry out the gods' orders.

In the final episode, Ulysses and his companions reach the Kingdom of Hades. They meet Orpheus, who seeks Ulysses' help to find his love, Eurydice, who has been taken to the Kingdom of Hades by Charon. Hades, the god of death, tells Ulysses that he must leave his companions behind if he wishes to return to Earth. He rejects the offer, which was a final test, and they all return home.