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Using the results of the calculation of the one-loop effective action (E.Elizalde et al , Phys.Rev. D49 (1994) 2852), we find the trace anomaly for mostgeneral conformally invariant 2D dilaton coupled scalar-dilaton system (thecontribution of dilaton itself is included). The non-local effective actioninduced by conformal anomaly for such system is found. That opens newpossibilities in generalizing of CGHS-like model for the study of back reactionof matter to 2D black holes.Comment: 6 pages, latex, no figur

Trace Anomaly and Nonlocal Effective Action for 2-D Conformally Invariant Scalar Interacting with Dilaton