Higher Order Power Corrections in Inclusive B Decays

We discuss order 1/m_b^4 and 1/m_b^5 corrections in inclusive semileptonic decay of a $B$ meson. We identify relevant hadronic matrix elements of dimension seven and eight and estimate them using the ground-state saturation approximation. Within this approach the effects on the integrated rate and on kinematic moments are estimated. The overall relative shift in V_{cb} turns out about +0.4% as applied to the existing fits. Similar estimates are presented for B -> X_s+\gamma decays.