  We present a description of the equivariant $K$-theory of a smooth projective
spherical variety. This provides an integral $K$-theory version of Brion's
calculation of equivariant Chow-cohomology of such varieties. We consider the
equivariant $K$-theory of wonderful compactifications of minimal rank symmetric
varieties. We obtain a formula for their structure constants in terms of
certain lower dimensional Schubert classes. This generalizes results of Uma on
equivariant compactifications of adjoint groups.
