  In an induced-gravity model, the stability condition of an inflationary
slow-rollover solution is shown to be $\phi_0
\partial_{\phi_0}V(\phi_0)=4V(\phi_0)$. The presence of higher derivative terms
will, however, act against the stability of this expanding solution unless
further constraints on the field parameters are imposed. We find that these
models will acquire a non-vanishing cosmological constant at the end of
inflation. Some models are analyzed for their implication to the early
universe.
