Abstract. In this paper some properties of weak regular injectivity for S-posets, where S is a pomonoid, are studied. The behaviour of different kinds of weak regular injectivity with products, coproducts and direct sums is considered. Also, some characterizations of pomonoids over which all S-posets are of some kind of weakly regular injective are obtained. Further, we give some Baer conditions which state the relation among some kinds of weak regular injectivity.
