  Let X be a complex nonsingular affine algebraic variety, K a holomorphically
convex subset of X, and Y a homogeneous variety for some complex linear
algebraic group. We prove that a holomorphic map f:K-->Y can be uniformly
approximated on K by regular maps K-->Y if and only if f is homotopic to a
regular map K-->Y. However, it can happen that a null homotopic holomorphic map
K-->Y does not admit uniform approximation on K by regular maps X-->Y. Here, a
map g:K-->Y is called holomorphic (resp. regular) if there exist an open (resp.
a Zariski open) neighborhood U of K in X and a holomorphic (resp. regular) map
h:U-->Y such that h|K=g.
