The results of our research presented in this paper are two-fold. First, an estimation of global posteriors is formalized in the framework of hybrid HMM/ANN systems. It is shown that hybrid HMM/ANN systems, in which the ANN part estimates local posteriors, can be used to modelize global model posteriors. This formalization provides us with a clear theory in which both REMAP and "classical" Viterbi trained hybrid systems are uni_ed. Second, a new forward- backward training of hybrid HMM/ANN systems is derived from the previous formulation. Comparisons of performance between Viterbi and forward- back- ward hybrid systems are presented and discussed.