[en] The authors have calculated the first non-linear corrections to the period shift and Q factor of a torsional oscillator containing a film of helium. To do so they have solved the Fokker Planck equation for the distribution of vortex pairs in the presence of an oscillating superfluid velocity field. The non-linear response is predicted to be proportional to v_n² for low values of the normal fluid velocity, v_n, which is in good agreement with the experimental results of Adams and Glaberson. For temperatures above the Kosterlitz Thouless transition temperature, T_KT, the ratio of the correlation length ξ₊ to the diffusion length becomes important in describing the temperature dependence of the non-linear response. The authors predict how the non-linear response depends on this ratio in the region where the ratio is large. 10 refs., 9 figs