McCauley has recruited two brothers, Major Nick Alborg, and Lt. Colonel Bill Alborg, who have demonstrated the ability to work together as if they had one mind. He needs them for the first refueling operation in space, and goes to their home to meet with them. They introduce him to their mother, Bill’s wife Dorothy, and Nick’s fiancée Helen. Mrs. Alborg is satisfied with her sons but admits she’ll be happy to have them at home when they stop flying. She invites McCauley to join them for dinner and he promises to come back for another dinner after the test. Well aware of the danger, Mrs. Alborg hesitates and then tells her sons to get moving. Once they leave with their women, McCauley notes that they make a fine team together. Mrs. Alborg asks if he has a family and he assures her that he understands what she’s going through.
Later, McCauley, Nick, and Bill arrive at the fuel transfer station and the colonel explains how dangerous the propellant is. They meet with Colonel Stoner, who explains that General Warren wants him to demonstrate the nature of the propellant. The brothers are well versed on the fuel ingredients, reciting it in chorus, and they meet with Warren. Warren explains to some touring dignitaries that the tanker will make two orbits. McCauley will intercept the tanker in the R101 on the second orbit. Stoner demonstrates the hydrazine and tetroxide fuel mixture, carefully setting off a small explosion to show how dangerous it can be. Warren finishes the demonstration and McCauley and the Alborgs leave for the pre-flight check.
An hour later, Tanker Abel off first with Nick and Stoner aboard. They take the tanker into a planned orbit, while McCauley and Bill make a carefully timed departure shortly thereafter. The early procedures go as planned and Tanker Abel enters the orbit. McCauley picks up the tanker on scope and closes in. Stoner and McCauley leave their respective ships and McCauley brings the refueling hose across to the tanker. The brothers then begin the fuel transfer but the tanker starts to oscillate because of the fuel pressure. As they try to release the hose, the two ships slam into each other repeatedly.
McCauley and Stoner try to free the hose without success but realize that the coupling is jammed. The tanker’s hull is penetrated and the fuel tanks start leaking. McCauley has the brothers shut down the valves and then tries to call Nick, but gets no response. Bill calls his brother, who returns to his chair and tells Bill that he was checking the tank bays. Mission Control makes contact and Nick tells them that they a leak and the ships are still connected due to the hose.
Bill puts a power wrench into the airlock and McCauley uses it to try and free the hose coupling. As the collisions continue, a tetroxide tank gives and McCauley tells Nick to relay a full report so that the next mission can avoid the same problem.
On the ground, Helen and Dorothy are having lemonade with their mother and Dorothy has a sudden impending sense of doom.
The hydrazine continues leaking and McCauley crosses over to examine the damage while Stoner continues work on the coupling. The two ships swing together again and McCauley leaps clear just in time and then drops back down. One of the ribs has come loose and will shear the flow pipe on the next collision. Stoner has two more bolts to free and McCauley discovers that his pack has caught on the rib. The two ships swing back together and Bill tells Nick that they have to activate a thrust at the same instant. The brothers pull it off, separating the ships and saving McCauley, and then Nick leaves the tanker and frees McCauley before the ships can come together again.
The last impact severs the flow pipe and Stoner frees the hose. Stoner, McCauley, and Nick board the R101 and Bill pulls away in the tanker. The astronauts watch as the hydrazine reaches critical and the tanker explodes. McCauley reports to Warren that they should use a rigid pipe instead of a flexible to maintain ships’ positions, and asks for reentry instructions.
Later, McCauley visits the Alborgs again and Bill notes that his brother was perfectly calm. Nick and Helen pull up and admit that they ran out of gas.