  Semileptonic decays of doubly heavy baryons are studied in the framework of
the relativistic quark model. The doubly heavy baryons are treated in the
quark-diquark approximation. The transition amplitudes of heavy diquarks bb and
bc going respectively to bc and cc are explicitly expressed through the overlap
integrals of the diquark wave functions in the whole accessible kinematic
range. The relativistic baryon wave functions of the quark-diquark bound system
are used for the calculation of the transition matrix elements, the Isgur-Wise
function and decay rates in the heavy quark limit.
