Let G/H be a pseudo-Riemannian semisimple symmetric space, with H connected. Let K be a maximal compact subgroup of G. The author constructs a system of fundamental weights for the H-K spherical finite- dimensional representations of G. Similar results have been obtained before by Oshima, Sekiguchi and Hoogenboom. This result is used to describe the union of the open orbits under the action of a minimal parabolic subgroup of G on G/H. If there is more than one open orbit, and if G/H is a space of type \(G_{{\mathbb{C}}}/G_{{\mathbb{R}}}\), then G/H is not a generalized Gelfand pair. This result might be generalized considerably if one focusses on parabolic subgroups associated to G/H in a canonical way rather than on minimal parabolic subgroups.