Beldar and Prymaat are emissaries from Remulak, a planet within the Cone Nebula 26 light years from Earth. They belong to a civilisation intent on expanding its empire by enslaving the populations of other worlds. The Coneheads' mission: conquer the Earth.

When a wrong turn at Machu Pichu crash-lands them in the middle of New York's East River, Beldar and Prymaat find themselves stranded and forced to assimilate into mainstream America. With INS agents in hot pursuit of these most unexpected of 'illegal aliens', the Coneheads find safe haven in Paramus, New Jersey, where they become typical hard-working parents raising their 16-year old daughter Connie.