  It is proved that if $G$ is a compact Lie group, then an equivariant Serre
fibration of $G$-CW-complexes is an equivariant Hurewicz fibration in the class
of compactly generated $G$-spaces. In the nonequivariant setting, this result
is due to Steinberger, West and Cauty. The main theorem is proved using the
following key result: a $G$-CW-complex can be embedded as an equivariant
retract in a simplicial $G$-complex. It is also proved that an equivariant map
$p: E \to B$ of $G$-CW-complexes is a Hurewicz $G$-fibration if and only if the
$H$-fixed point map $p^H : E^H \to B^H$ is a Hurewicz fibration for any closed
subgroup $H$ of $G$. This gives a solution to the problem of James and Segal in
the case of $G$-CW-complexes.
