  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 then
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.
