  The spectroscopy of the doubly heavy baryons including different heavy quarks
is studied based on the heavy quark symmetry of QCD. We point out that, when
the two heavy quarks are in $S$-wave, these baryons with a certain spin $j_l$
of the light cloud can be classified into two sets: a heavy quark singlet with
total spin of $j=j_l$ and a heavy quark multiplet with $j= (j_l+1) , j_l
,\ldots \vert j_l-1\vert$, all the baryons in these two sets have the same mass
and, the baryons with the same quantum numbers in these two sets do not mix
with each other. We finally point out that the strong decay of the first
excited baryon with light spin $j_l = 1/2$ to the ground state and one-pion is
determined by the mass splitting through the generalized Goldberger--Treiman
relation.
