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We calculate the radiative corrections to the nonleptonic inclusive B decay mode $b\rightarrow c\bar u d$ taking into account the charm quark mass. Compared to the massless case, corrections resulting from a nonvanishing c quark mass increase the nonleptonic rate by (4--8)\%, depending on the renormalization point. As a by--product of our calculation, we obtain an analytic expression for the radiative correction to the semileptonic decay $b\rightarrow u\tau\bar\nu$ taking into account the $\tau$ lepton mass, and estimate the c quark mass effects on the nonleptonic decay mode $b\rightarrow c\bar c s$.