Final answer:
The Cuban Missile Crisis in 1962, which involved a tense standoff between the U.S. and the Soviet Union over the presence of Soviet missiles in Cuba, brought both nations closest to nuclear war in the post-WWII period.
Step-by-step explanation:
The event in the post-WWII period that probably brought the United States and the Soviet Union closest to nuclear war was the Cuban Missile Crisis in 1962. This crisis involved a tense confrontation between the United States and the Soviet Union over the presence of Soviet intercontinental ballistic missiles in Cuba, a mere 90 miles from U.S. shores. The world watched in fear for 13 days as both superpowers seemed on the brink of starting a nuclear war. Through diplomatic negotiations, however, the crisis was resolved when the Soviets agreed to dismantle their missiles in Cuba, and the U.S., in turn, assured the Soviets that it would not invade Cuba.
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