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We prove that for any stratified fibre bundle p:A-~M (A being the underlying space of an abstract prestratification and M a smooth manifold) and any tr~ngulation of M there exists a triangulation of A such that p becomes linear with respect to these triangulations. In particular, any abstract prestratification is triangulable. As a corollary we obtain that the orbit space of a smooth action of a compact Lie group is triangulable.The purpose of this paper is to give an affirmative answer to the following problem: given a stratified fibre

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Let G be a compact Lie group and M be a smooth G-space. We prove that the real cohomology algebra of the orbit space M/G is isomorphic to the homology algebra of the de Rham complex of G-basic differential forms on M.