Michael Armstrong (Paul Newman), a rocket scientist from the United States, is attending a science conference together with his fiancée Sarah Sherman (Julie Andrews) in Copenhagen. He begins to act very strangely and Sarah follows him across the Soviet border to find out that he tries to defect to the enemy's side and sell off secret scientific information. However, it wouldn't be a movie directed by "the master of suspense", Alfred Hitchcock, if there wasn't a twist revealing that things are different than they appear...