PONNO A.,GALGANI L., GUERRA F. An analytical estimate of stochasticity thresholds in Fermi-Pasta-Ulam and $\phi^4$ models. (327K, PostScript) ABSTRACT. We consider an infinitely extended FPU model, and we show that the slow modulating amplitude of a narrow wave packet asymptotically satisfies the Nonlinear Schrodinger equation (NLS). It is well known that NLS presents a threshold below which the packet width remains narrow. We give an analytical estimate of such a threshold; we also make a comparison with the numerical results known to us, and show they are in remarkable agreement with our estimate. Analogous results are found for the $\phi^4$ model.