This paper is concerned with statistical estimation of total second order responses including the slow drift oscillation of a moored floating offshore structure in random seas. Stochastic interference between a wave frequency response and the slow drift oscillation affecting on the probability distribution is discussed. Assuming that the responses are represented in the form of two term Volterra functional series, an extended theory of probability density functions of an instantaneous response and its maxima are developed from the previous paper. It is applied to sway of moored floating semi-circular and rectangular cylinders, and confirmed its accuracy comparing with the exact solution in case of a pure second order motion at first. Next, non-normality of the total second order motion is investigated. It is shown that it is significant especially in case of heavy damping of the system and totally different from non-normality of the pure second order motion. The interference between the first and second order responses plays important roles on the probability density and the extreme value of the total response.