Nonminimal derivative couplings and inflation in generalized theories of gravity

We study extended theories of gravity where nonminimal derivative couplings of the form R-kl phi, (k) phi, (l) are present in the Lagrangian. We show how and why the other couplings of similar structure may be ruled out and t hen deduce the field equations and the related cosmological models. Finally , we get inflationary solutions which do follow neither from any effective scalar field potential nor from a cosmological constant introduced "by hand ", and we show the de Sitter space-time to be an attractor solution.