  We will provide a lower bound for the equivariant Lusternik-Schnirelmann
category of an arbitrary proper action in terms of the stratification by orbit
types, and an upper bound for proper polar actions in terms of the equivariant
Lusternik-Schnirelmann category of its generalized Weyl group. As an
application we reprove a theorem of Singhof that determines the classical
Lusternik-Schnirelmann category for U(n) and SU(n).
