  We construct a q-model structure, a h-model structure and a m-model structure
on multipointed $d$-spaces and on flows. The two q-model structures are
combinatorial and 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 multipointed $d$-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.
