The first and higher harmonic components of the resonant fluid response in the gap between two identical fixed rectangular boxes are experimentally investigated in a wave basin. Gap response is excited by transient wave groups (being based on scaled versions of the autocorrelation function of sea-state spectra, representing NewWaves, the average shape of large waves in a sea state). Several different wave groups with different maximum surface elevations, spectral peak frequencies and bandwidths are used, while the bilge shape of the boxes and approach angle of the waves are also varied. Unlike a simple regular wave, it is complicated to separate the harmonic components for a transient wave group due to nonlinear wave-wave and wave-structure interactions. A four-phase combination methodology is used to separate the first four harmonic components, and this also allows higher harmonic components to be isolated with simple digital frequency filtering. Harmonic components up to 14th order in the incident wave amplitude have been extracted. It is shown that for an incident group with appropriate frequency content, the linear gap response may be substantially smaller than the second harmonic component, which is strongly driven via quadratic coupling of the linear terms from the incident wave and occurs in the gap resonant modes. Double frequency excitation may have important practical implications for offshore operations. Fourth and zeroth (long-wave) harmonics in the gap are further driven via quadratic coupling of the second harmonic itself. Linear damping coefficients for the first few modes of the gap resonant response are derived from measured time series using a numerical fit and shown to be higher than those from linear diffraction calculations.