The nonlinearity of the surface impedance 2, of YBazCu307-= is of great importance for passive microwave devices. Since the 2, depends upon the microwave current and magnetic field H d , designs must consider the losses and intermodulation distortion at the operating power levels. We present a complete characterization of the nonlinearities in high-quality YBazCu307-, thin films. We have measured Z,(Hd) for Hd from 0 to approximately 1 kOe vs temperature from 4.2 K to T, and vs frequency from 1.5 to 10 GHz using a stripline resonator. The results are compared to a coupled-grain model which shows good agreement for R , ( H d ) . The imaginary part of Z,(Hd), i.e., X , ( H d ) , however, does not fit the model.