In the previous paper, the 1st-order motion responses of semi-submersibles in short-crested directional spectra waves were investigated. This paper presents results of an investigation into the 2nd-order responses such as slow drift oscillations in directional waves. Model tests in various kinds of directional waves which have specified power spectra and directional spreading, were carried out with spring moored and catenary moored conditions. Test results in directional waves are compared with those in uni-directional (long-crested) waves, and the influence of wave directionality on drift forces, low-frequency oscillations etc. are investigated. In order to estimate the 2nd-order responses in directional waves, new practical methods are proposed. These are based on the Pinkster's expression' of the low-frequency drift force spectrum in directional waves. By approximating the estimation of quadratic transfer functions of the mean drift force in two-directional cross regular waves, mean and low-frequency drift forces in directional spectra waves can be estimated practically. The applicability of these methods are investigated by comparing estimated 2nd-order sway responses with experimental measurements.