We shall show that endomorphism kernel property (EKP) and strong endomorphism kernel property (SEKP) are for some classes of universal algebras preserved by finite direct products and also by a special form of infinite direct sum construction. Full characterization of finite relative Stone algebras and L-algebras which have SEKP is given and a wide class of infinite relative Stone algebras which possess SEKP is described.

(strong) endomorphism kernel property, congruence relation, direct sum, factorable congruences.