A class of modified hydrophilic prepolymers and polymers is disclosed which are characterized by their specific reactivity. Isocyanate-capped oxyethylene-based prepolymers are modified by reacting with a compound having an isocyanate-reactive group which is a sulfhydryl group, an amino group, a hydroxyl group or a carboxyl group, and a non-isocyanate-reactive group, in quantities sufficient to modify at least a portion of the isocyanate groups of the prepolymer. Where said first functional group is an amino group contained in a diamine or polyamine compound or is a carboxyl group, the modifying compound is present in quantities sufficient to modify all or substantially all of the isocyanate groups of the prepolymer.