The authors analyse the saturation mechanism for the electrostatic plasma wave excited by two electromagnetic waves, and show that the level is determined not only by the relativistic frequency shift but also by other nonlinear effects which are of the same order. The difference between this and previous results, which suggest that there is only a relativistic frequency shift, arises from the boundary conditions imposed on the plasma. They do not impose a condition of zero current as others have, but instead argue that the correct condition to be imposed is that the average Eulerian velocity be zero. The analytic results are directly checked by numerical simulation carried out using a 1-D particle in cell code showing excellent agreement between the two approaches.