With the development of floating wind farms, the understanding of the far wake becomes of utmost importance because it cannot only be based on the experience acquired on fixed offshore turbine as the range of motion of the floater due to met-ocean conditions is in the same order of magnitude compared to the energetic turbulent scales of the atmosphere and to the characteristic scales of the wake. The objective of this wind-tunnel experiment is to analyse the behaviour of the wake center of a floating turbine subject to imposed surge motion. The experiment is carried out in the LHEEA wind tunnel where a 1/500 scale wind turbine model is immersed in a realistic offshore atmospheric-boundary layer. The model is actuated in surge by a linear motor able to reproduced idealised second order surge motion of a floating platform (mainly due to the waves) with a realistic amplitude and range of frequencies. Stereoscopic particle image velocimetry measurements are performed at two planes normal to the free-stream at distances of 4.6 and 8.1 diameters downstream of the turbine. Instantaneous velocity fields acquired at 14.1 Hz are individually analysed by convolution to find the location of the wake center. Results show that the wake center spreading is largely influenced by the downstream distance and only slightly affected by the surge motion. However, when analysing the wake position time series by a power spectral density, the signature of the surge motion becomes very clear for both downstream distances. These findings tell that the far wake (at least up to 8.1 diameters downstream) of a floating wind turbine has a “memory” of the motion in its frequency content. When extrapolating to a floating wind farm, this result suggests that a turbine inside a floating wind farm will be immersed in a flow including a significant dynamic signature in the range of its own motion.