The complete set of Maxwell's equations coupled by means of intrinsic nonlinearities in Kerr-type media has been analyzed and the integrated power flux has been found as a function of refractive index for hybrid TE-TM nonlinear surface waves. We demonstrate that for a fixed refractive index the electric-field vector of the nonlinear surface waves rotates with an adiabatic increase of the power flux from pure TE polarization at the threshold to pure TM polarization at the cutoff, passing through all possible hybrid polarization states for intermediate power fluxes.