Analysis of IgM by crossed immunoelectrophoresis is possible if the original technique is modified by the use of: agarose gel with little, or preferably no, electroendosmosis; a high pH of 10.3; and an antibody population essentially isoelectric at pH 10.3. Such an antibody population can easily be produced by a chemical modification, under mild conditions, of about one-third of the carboxylic acid groups of the antibodies. This analytical system also permits rapid quantitation of IgM by the electroimmunoassay.