Equations are derived which govern modulation of a continuous wave whistler mode transmission by gyroresonant electrons in a region limited in spatial extent. This model is similar to that used to explain the qualitative features of discrete VLF emissions in the geomagnetosphere. It is found that nonlinear wave-particle interaction results in amplitude modulation of the wave. An integral equation is then derived for the amplitude of the signal leaving the region. Numerical solutions of this equation for a loss cone electron distribution and for parameters typical of the geomagnetosphere at L=3 result is quasiperiodic pulsations in the amplitude for sufficiently high densities of resonant electrons. The frequency of these pulsations is in the several-hertz range, consistent with observations. Similarities of and differences between these calculations and previous theoretical studies of 'key-down' transmissions are discussed.