Let G be a locally compact Hausdorff group. It is proved that: (1) on each Palais proper G-space X there exists a compatible family of Ginvariant pseudometrics
(2) the existence of a compatible G-invariant metric on a metrizable proper G-space X is equivalent to the paracompactness of the orbit space X/G
(3) if in addition G is either almost connected or separable, and X is locally separable, then there exists a compatible G-invariant metric on X.