G-fibrations and twisted products

We prove that the functor of twisted product G×H− takes H-fibrations to G-fibrations when G is a compact metrizable (not necessarily Lie) group and H is its closed subgroup. This result is applied to the study of strong G-fibrations. In particular, we show that every G-map E→G/H is a strong G-fibration provided that E is a G-fibrant space.