  We consider the category of presheaves of Gamma-spaces, or equivalently, of
Gamma-objects in simplicial presheaves. Our main result is the construction of
stable model structures on this category parametrised by local model structures
on simplicial presheaves. If a local model structure on simplicial presheaves
is monoidal, the corresponding stable model structure on presheaves of
Gamma-spaces is monoidal and satisfies the monoid axiom. This allows us to lift
the stable model structures to categories of algebras and modules over
commutative algebras.
