  A quark model is applied to the spectrum of baryons containing heavy quarks.
The model gives masses for the known heavy baryons that are in agreement with
experiment, but for the doubly-charmed baryon Cascade_{cc}, the model
prediction is too heavy. Mixing between the Cascade_Q and Cascade_Q^\prime
states is examined and is found to be small for the lowest lying states. In
contrast with this, mixing between the Cascade_{bc} and Cascade_{bc}^\prime
states is found to be large, and the implication of this mixing for properties
of these states is briefly discussed. We also examine heavy-quark spin-symmetry
multiplets, and find that many states in the model can be placed in such
multiplets. We compare our predictions with those of a number of other authors.
