We study anomalous Wess-Zumino couplings of D-branes and O-planes in a general background and derive them from a direct string computation by factorizing in the RR channel various one-loop amplitudes, In particular, we find that Op-planes present gravitational anomalous couplings involving the Hirzebruch polynomial (L) over cap, similarly to the roof genus (A) over cap encoding Dp-brane anomalous couplings, We determine, in each case, the precise dependence of these couplings on the curvature of the tangent and normal bundles. (C) 1999 Elsevier Science B.V. All rights reserved.