The dianhydride monomer 1,4-phenylenebis (phenylmaleic anhydride) was polymerized with various aromatic diamines in a one-step solution polymerization to afford high molecular weight, soluble polyimides containing backbone phenylmaleimide structures. The polyimides were soluble in amide solvents, chlorinated hydrocarbons, and tetrahydrofuran at 25-degrees-C at a concentration of 15% (w/v), displayed molecular weight distributions (M(w)/M(n)) of 2.0-2.2 as determined by absolute GPC and showed T(g) values of 240-degrees-C and above as measured by differential scanning calorimetry. In addition, polyimide thermosets were prepared from these materials by thermal cure at 350-360-degrees-C. The crosslinked polyimides displayed T(g)s 20-25-degrees-C higher than their soluble precursors, and chloroform extraction indicated gel fractions ranging from 74-100% after cure.