Investigations are presented, on some effects of nonlinearity in the motion of shallow water wave spectra. The waves were generated, mechanically in a laboratory wave flume with fixed bottom. Essential differences with the linear dispersion relation are found, showing vanishing dispersivity of higher frequency spectral components in strongly nonlinear spectra. The mean frequency increases with decreasing water depth. The relation of the peak frequency to the mean frequency varied in the experiments from 0.9 to 0.5, for deep to shallow water wave spectra respectively.