The nonlinear responses of a one-dimensional quasiperiodic Fibonacci structure containing single negative materials (linear mu-negative and Kerr-type nonlinear epsilon-negative layers) were investigated using the transfer matrix approach. Bistable behaviors were found in the considered Fibonacci structure. The results indicate that transmission in the zero phase gap regions is relatively insensitive to the angle of incidence, in comparison with the one in the Bragg gap. Transmissions associated with the zero phase gap especially peak at almost the same input intensity for different angles of incidence. The effect of the loss and the scaling on the characteristics of bistability were considered in both gaps. The zero phase gap soliton is insensitive to the angle of incidence and loss factor.