Homopolyimides and copolyimides of aromatic tetracarboxylic acids and aromatic diamines which are substituted in the two ortho-positions relative to at least one N atom by alkyl, alkoxy, alkoxyalkyl, cycloalkyl or aralkyl, are soluble in organic solvents and have increased glass transition temperatures and hence very good heat stabilities. Such polyimides, which contain radicals of a benzophenonetetracarboxylic acid, are radiation-sensitive and autophotocrosslinkable. The polyimides are suitable for the production of films, protective coatings and photographic relief images.