Novel compositions comprising unsaturated polyhemi-amic acid compositions and processes for their preparation are disclosed herein. These new compositions are primarily derivatives of anhydride-terminated aromatic polyimides from which they are prepared by amidation to provide unsaturated amide groups having terminal --CH.dbd.CH.sub.2 groups as hemi-amic acid groups or their derivatives. These new compositions are more tractable than the original anhydride-terminated polyimides and can be converted at appropriate lower temperatures to crosslinked, insoluble, infusible polymers without by-product formation thereby extending greatly the applications for which the aromatic polyimides can be employed. Also included are monomeric compounds containing unsaturated amide groups derived from monomeric tetracarboxylic dianhydrides. These are particularly useful as crosslinking agents.