Introducing the notion of the local thermal equilibrium,the Hawking effect and the entropy of a nonstationary Kerr-Newman black hole whose metric changes slowly are studied by the method of Damour-Ruffini and the thin film model.First,we obtain the Hawking radiation temperature and the thermal spectrum formula,and show that the Hawking temperature depends on the time and the location on the event horizon,the thermal spectrum is a quasi-black-body's thermal spectrum.Second,we calculate the black hole entropy,which is just the Bekenstein-Hawking entropy with the same geometrical cutoff relationship as in the static and spherical case.The results show that the temperature of the black hole is a local quantity,and the entropy of the nonstationary black hole is also proportional to the horizon area as in the case of stationary black holes.