Saturated and ethylenically unsaturated compounds containing carboxylic, amino or alcohol groups are reacted under mild conditions and in short process times with polycarbodiimides containing free isocyanate units to provide polymers with excellent properties. The unsaturated groups bonded to the polymers are particularly important because these groups provide reactive centers that can be crosslinked, either thermally or in the presence of catalysts that initiate polymerization or by radiation. The polymers can also be crosslinked either alone or by copolymerization with various unsaturated monomers. The resulting crosslinked or cured resins provide excellent properties such as hardness, high elongation, excellent toughness, high heat distortion temperatures and good corrosion resistance.