Abstract: "Intermediate model structures for simplicial presheaves", by J.F. Jardine This note (it is not really a finished paper) shows that any set of cofibrations containing the standard set of generating projective cofibrations determines a closed model structure on the category of simplicial presheaves on a small Grothendieck site, for which the weak equivalences are the local weak equivalences in the usual sense. A condition is given for these new model structures to be cofibrantly generated; this condition is met by Blander's local projective theory. Department of Mathematics University of Western Ontario London, Ontario N6A 5B7 Canada URL: http://www.math.uwo.ca/~jardine/papers/