New statistical theory was developed by the authors in the previous paper, which gives probability density function (p. d. f.) and extreme values of total second order responses of moored vessels in random seas. It assumes the response represented in the form of two term Volterra functional series and is based on the generalized Laguerre polynomial expansion of p. d. f. of which the first term is a gamma p. d. f. consisting of three parameters. This paper shows non-normality of surge responses of moored tanker and semi-submersible measured in a wave basin, and determines that the theory estimates it very well. Furthermore effect of time varying wave drift damping and other slow motion hydrodynamic force coefficients on p. d. f. and extreme values are discussed by time domain simulations. This effect cannot be represented in the form of two term Volterra functional series.