  We prove a version of the BKK theorem for the ring of conditions of a
spherical homogeneous space $G/H$. We also introduce the notion of ring of
complete intersections, firstly for a spherical homogeneous space and secondly
for an arbitrary variety. Similarly to the ring of conditions of the torus, the
ring of complete intersections of $G/H$ admits a description in terms of
volumes of polytopes.
