This paper presents statistical analyses for second-order responses of tension-leg platform. Second-order responses of moored vessels in random seas include two kinds of elements, difference-frequency response and sum-frequency response. It is well known that difference-frequency response leads to slow drift oscillation. Sum-frequency response is generally eliminated for an analysis of slack mooring. In the case of heaving motion of tension-leg platform, sum-frequency response is large because of its high natural frequency, and it leads to springing response. Non-normality of two kinds of responses are investigated, and compared these two responses for surging, heaving and pitching modes. Main results are as follows : 1) Sum-frequency response of exciting force is a little larger than difference frequency response of it. Both of them have large non-normality. 2) Sum-frequency response of heaving and pitching motions are much larger than difference, and surging shows opposite result. These three large responses have behavior similar to normal distribution. 3) Gamma-distribution approximation and DVI method can be applied to sum-frequency response. 4) Non-normality increases and standard deviation becomes small as damping increases.