North Sea wave records, obtained in conditions of active wave generation, have been analyzed with respect to the distribution of the length of wave groups. The results are compared to a theory by Kimura, in its original form as well as with the addition of a new spectral wave groupiness parameter, based on the theory of Gaussian processes. The results lend support to the validity of Kimura's theory, this in turn implies further evidence that the phenomenon of wave groups in sea waves can by and large be explained, both qualitatively and quantitatively, in terms of the linear, random phase model for the wave motion, even in conditions of active wave generation.