As Koenig and his staff finish up their meeting, Commissioner Simmonds complains that they're wasting their efforts simply trying to survive when they should be finding a way back to Earth. Koenig refuses to hear it, insisting it's impossible, and Dr. Russell warns that there's no point in trying to build up false hope. They're interrupted when Moonbase Control detects a manned spaceship on a collision course.
Carter takes out two Eagles to intercept the alien ship and determines that it's out of control. They watch as it makes a rough landing on the lunar surface. Koenig takes a team out to investigate and ignores Simmonds' suggestion that he should go along with them. They take a rescue pod out and attach it to the alien spacecraft, and then enter through a hatch. There's no atmosphere or gravity inside but they find six aliens locked in glass caskets. Once they establish a sustainable atmosphere, Dr. Russell examines the bodies but can find no trace of life. Even frozen hibernation wouldn't so thoroughly mute life signs. She decides to risk opening one of the caskets. There's an explosion and the occupant is reduced to dust in an instant.
The ship's systems start to activate and the other five aliens awake. Dr. Russell tries to apologize to their leader, Zantor, but he simply takes her by the hand and guides her and the others over to the casket of their deceased comrade. They perform a mourning ceremony and silently invite the Alphans to participate.
At Moonbase Control, Simmonds paces nervously until Koenig finally calls to explain that the aliens will be bringing their spacecraft to the base. Simmonds rushes to the airlock and insists that Koenig introduce him. He identifies himself as the representative of Earth's authority. He offers a judicial hearing to punish whoever was responsible for the alien crewman's death but Zantor assures him that he is aware it was an accident and won't seek retribution. As Koenig has his people escort the aliens to quarters, Simmonds warns that they may not be as friendly as they seem.
Later, Zantor and the others give Koenig rare eggs from their home planet of Kaldor. Zantor explains that all life on Kaldor was dying off and the civilization sent out ships to any planets they believed could support them. Zantor's ship was programmed to land on the Moon and then his team would proceed to the planet below. The Kaldorian ship managed to home in on the Moon despite the fact it was no longer in orbit above the Earth. Simmonds wonders if they can still locate Earth using their navigational computers and Zantor admits that they can. The Kaldorians still wish to colonize Earth but would accept self-destruction if they were unable or the natives did not wish them there. Dr. Russell offers to check to make sure their bodies are compatible with Earth life, and Zantor is glad to have her help. As the Kaldorians leave, Simmonds tells Koenig that he needs to act as leader, seize the Kaldorian spaceship, and send six Alphans back to Earth.
Dr. Russell tests Zantor, who explains that they use a superior form of suspended animation that completely stops all bodily processes. As she runs her tests, Zantor explains that at their current location it will take them 75 years to reach Earth. Once her tests are complete, Russell returns to the ship with Zantor. He says that they can be ready to leave within 20 hours and offers to take one Alphan in the casket that held the now-dead Kaldorian. Koenig has Dr. Russell start testing to see if the process will accommodate human life forms. Simmonds continues to push for Koenig to simply take the ship and send six of their people back, but Koenig insists that only one Alphan will go back and the computer will randomly choose the person. When Simmonds pushes the matter and comments that he figures Koenig will include himself. The commander assures him that he won't put his own name into the selection, and he wonders if there's even a recognizable life for any of them to return to 75 years in the future.
Once she's sure that the process is safe, Dr. Russell uses herself as a test subject for the Kaldorian suspended animation. She fails to revive and Bergman informs Koenig that the doctor is now trapped in a coma. Zantor works with Dr. Mathias to revive her and they realize that the Moonbase computers don't allow for the existence of the soul. Koenig is forced to choose when Zantor warns him that revival could cause permanent brain damage. He authorizes Zantor to go ahead and Dr. Russell successfully revives.
The computer makes its selection but chooses three crew members. Koenig refuses to even read the list until Dr. Russell assures him that the suspended animation process is safe. Simmonds insists that Koenig should make the decision, not the computer, and that the commander should choose Simmons. Zantor arrives to make his farewells and Simmonds, unseen, switches his com-link for Koenig's and slips away.
Zantor explains that the problem with Dr. Russell is that the computer has to make a specific bio-matrix for the person selected. Once Koenig informs him who the chosen Alphan is, they'll make a new bio-matrix for him. Meanwhile, Simmons goes to the power station, stuns most of the technicians, and forces the one remaining one to open the power core chamber. Koenig realizes too late that Simmonds has switched comlinks. He contacts Simmonds, who threatens to destroy the converted unless he's designated the chosen passenger. With time and power running out, Koenig asks Zantor for permission to take Simmonds. The Kaldorian captain understands the situation and agrees to take Simmonds with him. The other Alphans heartily approve as long as they're rid of Simmonds. Simmonds is still suspicious and Zantor offers himself as a good-faith hostage.
Simmonds goes to the docking bay using Zantor as a hostage. The Kaldorian captain offers Koenig his best wishes and bemoans the fact that Simmonds is getting his way through force. Once they board the spacecraft, Simmonds forces Zantor and the other four to enter the suspension caskets first and then finally gets into his own. The mechanism activates, suspending all of them, and the spaceship lifts off on its 75-year trip for Earth.
Simmonds wakes up and realizes that he's healthy and unharmed. He tries to contact Earth using his comlink to notify them that he's arrived. On Moonbase Alpha, they hear Simmonds' transmission and realize he's only a few hours away. Because Zantor didn't have time to adjust the bio-matrix, the process didn't fully affect Simmonds. He's now trapped in the casket on a ship with no air, food, or water. When Simmonds checks the comlink, he realizes that only a few hours have passed and that he will die a slow painful death.
As the alien spaceship draws out of range with Simmonds trapped on board, Dr. Russell wonders who the computer chose to return to Earth. Koenig reveals that the computer chose Simmonds.