  The semileptonic decays of heavy spin--1/2, $\Xi_{b(c)}$ and $\Xi'_{b(c)}$
baryons to the light spin-- 1/2, $\Xi$ and $\Sigma $ baryons are investigated
in the framework of the light cone QCD sum rules. In particular, using the most
general form of the interpolating currents for the heavy baryons as well as the
distribution amplitudes of the $\Xi$ and $\Sigma $ baryons, we calculate all
form factors entering the matrix elements of the corresponding effective
Hamiltonians in full QCD. Having calculated the responsible form factors, we
evaluate the decay rates and branching fractions of the related transitions.
