We have measured the microwave surface impedance of thin films of YBa2Cu3O7-X as a function of temperature, frequency and rf magnetic field, H(rf), using a stripline-resonator technique. The films were deposited in situ by single-target off-axis magnetron sputtering. The frequency range was from 0.4 to 20 GHz, the temperature range from 4.2 K to T(c), and the rf magnetic field range from 0 to 30 Oe. The surface resistance R(S) at 4.2 K and 1.5 GHz is 4 x 10(-6)-OMEGA. The penetration depth is determined to be 0.167-mu-m in the best film. In some films R(S) shows a linear dependence on H(rf) and rises rapidly at large fields, showing no evidence of saturation. In others R(S) shows weak dependence on H(rf) before rising rapidly. These behaviors differ from those observed in bulk ceramic YBa2Cu3O7-X and in unpatterned films measured in microwave cavities. However, the shape of R(S)(H(rf)) for the YBa2Cu3O7-X films is similar to that of Nb and NbN films measured in the same stripline geometry. We discuss the effects of the current distributions in the resonator on the measured R(S)(H(rf)). We will also present measurements of the intermodulation products in the resonators and discuss the implications of the R(S) and intermodulation measurements for microwave device applications.