We present the results of experimental measurements of nonlinear microwave absorption in thin circular high-temperature superconducting YBCO films. The sample was located in a field of two waves - weak nonmodulated and strong modulated with rectangular pulses. A change in the absorption during a pulse was fixed. The effect was observed in the temperature range of 77.5 - 90.0 K. Microwave heating of the sample, Ginzburg - Landau nonlinearity, Abrikosov vortices and the Josephson effect were considered by a discussion of possible nonlinearity mechanisms. Numerical calculations showed that at weak incident power the Josephson nonlinearity was the only reason for the nonlinearity observed. The d.c. magnetic field up to 200 Oe did not change nonlinear interaction. This could be attributed to the compensation of the d.c. Meissner currents by Abrikosov vortices.