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Extreme wave-structure interaction in terms of wave run-up & air-gap requirement for a semi-submersible floating platform in a random sea is investigated experimentally. The ‘designer’ waves that lead to extreme run-up & air-gap responses are examined to study the reciprocity between the response|NewWave and the wave|NewResponse. Based on the phase-inversion method and linear transfer functions, the linear responses can be decomposed from the total signal, assuming that a description up to 2nd order is sufficiently accurate. We find that the air-gap response between the front legs of the model is accurately predicted using 2nd order decomposition and that the statistics of extreme crests and troughs are split symmetrically either side of the Rayleigh distribution. In contrast, wave run-up on an upstream leg of the structure is much more nonlinear, even without severe splashing. The 2nd order contributions are almost as large as the linear, and there are clearly large contributions from more nonlinear processes. In general, the 2nd order sum frequency contributions can be modelled using a narrow-banded frequency assumption.