With the Cold War becoming closers towards a nuclear war, a young boy wants Superman to help stopa nuclear war from happening. Lex Luthor breaks out of jail and creates a clone of Superman called Nuclear Man to do his evil bidding.
Trivia: Near the end of the film, Superman gives a press conference in front of a bluish mirror-glass building which is meant to be the Daily Planet skyscraper in Metropolis (which we all know is New York, sort of). The shot is framed so you can only see the bottom of the building - necessary as it is only about 3 floors high, and is in fact the railway station in Milton keynes, England, about 400 yards from where I work. Even the crowd have a vaguely British look about them - presumably passers-by were recruited and stood there in their own clothes (this would matter less now - Brits look more American than they did in the Eighties).