The story is set in a future 1964, in the months following World War III. The conflict has devastated the northern hemisphere, polluting the atmosphere with nuclear fallout and killing all life. While the bombs were confined to the northern hemisphere, air currents are slowly carrying the fallout south. The only areas still habitable are in the far southern hemisphere, like Australia. From Australia, survivors detect an incomprehensible Morse code signal from the United States in San Diego. With hope that someone is alive back home, the last American nuclear submarine, USS Sawfish, under Royal Australian Navy command, is ordered to sail north from Melbourne to try and make contact with the signal sender. The captain, Dwight Towers (Gregory Peck), leaves behind his good friend, the alcoholic Moira Davidson (Ava Gardner), despite his feelings of guilt about the death of his wife and children in Connecticut. Towers refuses to admit they are dead and continues to behave accordingly. The Australian government arranges for its citizens to receive suicide pills and injections, so that they end things quickly before there is prolonged suffering from the coming radiation sickness. An Australian naval officer, Peter Holmes (Anthony Perkins), has a baby daughter and a naive and childish wife, Mary (Donna Anderson), who is in denial about the impending disaster. Assigned to travel with the American submarine for several weeks, Peter tries to explain to Mary how to euthanize their baby and kill herself with the lethal pills in case he's not yet home. Mary, however, reacts violently at the prospect of killing her daughter and herself. One scientist's theory is that the radiation near the Arctic Ocean could be less than that at mid northern hemisphere. If so, this would indicate the radiation could disperse before reaching the southern hemisphere. This was to be explored along with the submarine's main mission. After sailing to Point Barrow, Alaska, they determine that radiation levels are intensifying. The submarine next stops at San Francisco. The views through the periscope show no signs of life and no damage to buildings. One crewman jumps ship to spend his last hours in his hometown. After attempting to convince the crewman to return, Towers accepts his decision. The crewman is last seen fishing and awaiting his death as the Sawfish submerges, never to return. Sawfish then travels to an abandoned oil refinery in San Diego, where they discover though everyone is dead, the hydroelectric power is still operating. The ship's communications officer is sent ashore in a radiation suit to investigate. The mysterious signal is the result of a Coca Cola bottle being bumped by a window shade fluttering in the breeze and tapping a telegraph key. Bitterly disappointed, the submariners return to Australia to live out the remaining time before the nuclear fallout arrives. They make their best efforts to enjoy what time and pleasures remain to them before dying. Scientist Julian Osborne (Fred Astaire) and others organize a wild motor race that kills several participants. Moira only sees the senselessness of the race, but when she asks Osborne why he is taking part, he responds, "because I want to". Prior to the submarine voyage to America, Towers told Moira about his enjoyment of the relaxation from fishing. During his absence, Moira gets the fishing season set earlier so Dwight will get one last chance to fish. With Towers now accepting the death of his family, they embark on a weekend trip. Retreating to the resort for the night, Dwight and Moira share a romantic interlude inside their room as outside a gathering storm howls. Returning to Melbourne, Towers is told one of his crew has developed radiation sickness. The deadly radiation has arrived. Some citizens seek spiritual guidance from the Salvation Army. They hang a banner from the public library exhorting that "There Is Still Time . . . Brother". Osborne, proud and satisfied after winning the Australian Grand Prix, seals himself and the car, engine running, inside a garage to set up his presumed suicide by carbon monoxide poisoning. Others line up to receive their suicide pills. Later, Mary Holmes (Donna Anderson) becomes emotionally unbalanced and must be placed under sedation. She regains lucidity, and she and Peter share a tender moment together before Mary decides that she has been "foolish and impractical" and asks her husband to "take care" of her and their daughter. "I'd like that cup of tea now," she tells him. Dwight wants to stay with Moira, but his remaining crew want to head for home and die in the United States. In the end, Captain Towers chooses not to stay but rather to lead his crew back to the States. Moira watches from the shore as the Sawfish submerges beneath the waves. The end shows the deserted, abandoned streets of Melbourne. The last shot, punctuated by emphatic music, is of the "There Is Still Time . . . Brother" banner.