In the present work we give a generalization, on the one hand, of the main result of [1] on the existence of weak solutions (in the sense of joint solution-measure) for equations with driving martingales and random measures the coefficients of which depend on the solution-processXat eachtεR+only throughXt–, and on the other hand, of the main results of [2] on the existence of weak solutions (in the strict sense) for equations the coefficients of which depend on the past ofXbut with driving semimartingales. Thus we prove existence of weak solutions (in the strict sense) for the equations with driving martingales and random measures coefficients of which depend in a predictable way on the processX. In the course of the proof the weak solution turns out as in [1] and [2] to be regular, that is satisfying the condition 7.4 or 7.5 of [2]