Title: Flow does not model flows up to weak dihomotopy Abstract: We prove that the category of flows cannot be the underlying category of a model category whose corresponding homotopy types are the flows up to weak dihomotopy. Some hints are given to overcome this problem. In particular, a new approach of dihomotopy involving simplicial presheaves over an appropriate small category is proposed. This small category is obtained by taking a full subcategory of a locally presentable version of the category of flows. Comments: 16pages, 3 figures Url: http://www.pps.jussieu.fr/~gaucher/ and ArXiv.