  The Standard Model predictions for the hadronic and leptonic electric dipole
moments (EDMs) are well far from the present experimental resolutions, thus,
the EDMs represent very clean probes of New Physics effects. Especially, within
supersymmetric frameworks with flavor-violating soft terms large and
potentially visible effects to the EDMs are typically expected. In this work,
we systematically evaluate the predictions for the EDMs at the
beyond-leading-order (BLO). In fact, we show that BLO contributions to the EDMs
dominate over the leading-order (LO) effects in large regions of the
supersymmetric parameter space. Hence, their inclusion in the evaluation of the
EDMs is unavoidable. As an example, we show the relevance of BLO effects to the
EDMs for a SUSY $SU(5)$ model with right-handed neutrinos.
