Batch, semicontinuous, and continuous versions of the parametric pump are analyzed in terms of an equilibrium theory of pump performance. The batch pump and pumps with feed at the enriched end are shown under certain conditions to have the capacity for complete removal of solute from one product fraction and at the same time arbitrarily large enrichment of solute in the other product fraction. Under other conditions and for all conditions for pumps with feed at the depleted end separation factors and enrichment are modest.