Under certain assumptions, a right continuous Markov process has a dual one with respect to some measure, this dual being left continuous [11]. Theorem 1 shows that, in the same case, it is possible, by simple transformations, to guarantee the right continuity of the dual process. Theorem 2 deals with conditions under which the killing of dual processes at the hitting time of a given set again results in dual processes. From Theorem 2 we get Theorem 3 containing the fundamental Hunt identity.