We have performed detailed CW NMR measurements on superfluid He-3-B in order to investigate stationary spin-wave modes in a texture veil. Our results at high temperatures are consistent with previous work. However, we find that the spin dynamics is profoundly modified, even for small excitation amplitudes, for temperatures on the order of 200 mu K, substantially lower than the limit reached in previous investigations. We report the observation of nea-linear spin-waves at ultra-low temperatures and their characterization in terms of a third-order anharmonic oscillator.