The relationships between generalized inverses of the product of two matrices A; B and the product of generalized inverses of A, B have been studied in the literature. By applying the product singular value decomposition (P-SVD), in this paper we derive equivalent conditions for B{1,2}A{1,2} subset of or equal to (AB){1,2}, (AS){1,2}subset of or equal to B{1,2}A{1,2}, B{1,2}A{1,2} = (AB){1,2}, and equivalent conditions for (AB){1} subset of or equal to B{1} A{1}, (C) 1998 Elsevier Science Inc. All rights reserved.27741699299311