The real and imaginary parts of the surface impedance of YBCO superconductors have been studied at different microwave power levels. Using the relations for the critical current density and the grain boundary resistance, a relation for calculating the power dependence of the surface resistance has been obtained. Also, a relation to find the resonant frequency of a superconducting microstrip resonator at various input power levels has been derived. Measurements have been carried out on various microstrip resonators to study the variation of surface resistance and resonant frequency at different rf power levels. The experimental results are in good agreement with theoretical results. ©1997 American Institute of Physics.