Compositions are described which are useful particularly in improving the electrodeposition of zinc from aqueous alkaline plating baths. In one embodiment, the new composition comprises the reaction product of(A-1) at least one nitrogen-containing heterocyclic compound with(A-2) at least one hydroxyamine;(A-3) an epihalohydrin, glycerolhalohydrin or mixtures thereof; and(A-4) at least one amino compound containing at least one N--H group to form the desired polymeric composition.Aqueous alkaline zinc electroplating baths containing the compositions of the invention with or without cyanide present, deposit a bright and lustrous zinc coating on metal over a wide range of current densities.