Using the results of the calculation of the one-loop effective action (E. Elizalde et al., Phys. Rev.D49, 2852 (1994)), we find the trace anomaly for most general conformally invariant 2-D dilaton coupled scalar–dilaton system (the contribution of dilaton itself is included). The nonlocal effective action induced by conformal anomaly for such system is found. That opens new possibilities in generalizing of CGHS-like model for the study of back-reaction of matter to 2-D black holes.