Water-in-oil emulsions of water-soluble ethylenically unsaturated amide monomers, alone or in the presence of acrylic acid or alkyl-substituted acrylic acid are continuously catalytically polymerized, or co-polymerized, in thin films or layers and in the absence of oxygen at temperatures maintained within plus or minus 3*C. of predetermined optimum polymerization or co-polymerization temperatures.