New crosslinkable polymers, in particular polymerization products of 5-maleimidyl-trimellitic acid derivatives and 3,5-bis-(maleimidyl)-phthalic acid derivatives and vinyl monomers and polycondensation products of the said imidyl compounds and diamines, diols or amino-alcohols and optionally a di-, tri- or tetra-carboxylic acid derivative are described. These polymers are distinguished by good processability and good solubility in customary organic solvents and are suitable for the manufacture of very diverse industrial products, such as thin and thick films and the like.