We calculate the next-to-leading order contribution to the masses of t
he heavy baryons in the bound-state approach for baryons containing a
heavy quark. These 1/N-C corrections arise when states of good spin an
d isospin are generated from the background soliton of the light meson
fields. Our study is motivated by the previously established result t
hat light vector meson fields are required for this soliton in order t
o reasonably describe the spectrum of both the light and the heavy bar
yons. We note that the inclusion of light vector mesons significantly
improves the agreement of the predicted hyperfine splitting with exper
iment. A number of aspects of this somewhat complicated calculation ar
e discussed in detail. (C) 1997 Elsevier Science B.V.