A comprehensive directional wave buoy data set showing the directional wave spectrum during the passage of a number of hurricanes is presented. The data confirm remote sensing measurements, showing that waves in the forward quadrants of the storm are dominated by swell radiating out from the intense wind regions to the right of the storm centre. The data show that for almost all quadrants of the storm, the dominant waves are remotely generated swell. The directional spectra are composed of swell at low frequency (the dominant waves) and locally generated waves above approximately three times the spectral peak frequency. There is, however, no tendency for the spectrum to become bi-modal in either frequency or direction. Rather, the spectra are directionally skewed, with a smooth directional transition from low frequency to high frequency. As for uni-directional wind field cases, the spectra are narrowest at the spectral peak frequency and broaden at frequencies above and below the peak. Despite the fact that much of the wave field is dominated by swell, the spectral width, as a function of non-dimensional frequency is very similar to that reported for uni-directional wind fields. The one-dimensional spectrum can be approximated by the parametric form proposed by Donelan et al. (1985). The parameters defining the spectrum also follow the same functional dependence as that reported for uni-directional winds. The fact that both the one-dimensional and directional spectra are very similar to spectra reported under simple uni-directional winds is interpreted as being a result of the shape stabilization effects of non-linear interactions. The data exhibit these same functional forms at low frequencies where they can be receiving no significant local input from the wind. This result indicates that the spectral shape is being controlled almost completely by the non-linear interactions with input and dissipation terms of lesser importance. This result indicates that input and dissipation are important in determining the total quantity of energy in the wave field, but appear to play only a minor role in determining the spectral shape.