  Popov has recently introduced an analogue of Jordan classes (packets, or
decomposition classes) for the action of a theta-group (G_0,V), showing that
they are finitely-many, locally-closed, irreducible unions of G_0-orbits of
constant dimension partitioning V. We carry out a local study of their closures
showing that Jordan classes are smooth and that their closure is a union of
Jordan classes. We parametrize Jordan classes and G_0-orbits in a given class
in terms of the action of subgroups of Vinberg's little Weyl group, and include
several examples and counterexamples underlying the differences with the
symmetric case and the critical issues arising in the theta-situation.
