six model categories for directed homotopy

We construct a q-model structure, an hmodel structure and an m-model structure on multi-pointed d-spaces and on flows. the two q-model structures are combinatorial and left determined and they coincide with the combinatorial model structures already known on these categories. the four other model structures (the two m-model structures and the two h-model structures) are accessible. we give an example of multi-pointed d-space and of flow which are not cofibrant in any of the model structures. we explain why the m-model structures, quillen equivalent to the q-model structure of the same category, are better behaved than the q-model structures.