Polyurethane polymers are made from a reaction mixture that contains a polyisocyanate, a hydroxylmethyl-containing fatty acid or ester, and another polyol, polyamine or aminoalcohol. The carboxylic acid or ester group on the hydroxymethyl-containing fatty acid or ester are capable of engaging in a variety of reactions with the polyisocyanate and/or amine or hydroxyl groups present in the reaction mixture. This allows for good quality, high molecular weight polymers to be produced even though the hydroxymethyl-containing fatty acid or ester tends to be a low functionality material.