  We present three-loop (NNNLO) corrections to the heavy-to-heavy quark
transitions in the limit of equal initial and final quark masses. In analogy
with the previously found NNLO corrections, the bulk of the result is due to
the beta_0^2 alpha_s^3 corrections. The remaining genuine three-loop effects
for the semileptonic b --> c decays are estimated to increase the decay
amplitude by 0.2(2)%. The perturbative series for the heavy-heavy axial current
converges very well.
