Free-electron lasers in the electron cyclotron frequency range have been proposed as an efficient means of heating and driving current in tokamak plasmas. The proposed free-electron laser will have short pulses (approx. =5 x 10/sup -8/ sec) with a peak power of (4--8) x 10Z W and electric fields within the plasma in the range 10V--10W V/cm. At these high intensities nonlinear effects compete with thermal effects in the absorption of microwave power. Analytic and numerical calculations of the nonlinear absorption are presented.