Observations of neutral winds from rocket release experiments within the premidnight and postmidnight substorm recovery phase aurora, show very large E-region neutral winds of several hundred m/s, where winds measured on the dusk side are even larger than those on the dawn side. These large winds are also associated with strong shears, and there is evidence that some of the regions below these shears may be unstable. The mechanisms which generate this strong vertical structure are not well understood. It is also not known whether the acceleration conditions in the pre and post midnight sectors of the aurora may produce significantly different neutral responses on the dawn and dusk sides. Simulations have been performed using a three-dimensional high resolution limited area thermosphere model to try to understand the neutral structure within the dawn and dusk side aurora. When simulations are performed using auroral forcing alone, for equivalent conditions within the dawn and dusk sectors, differences are found in the simulated response on each side. When measured values of auroral forcing parameters, and background winds and tides consistent with recent observations, are used as model inputs, some of the main features of the zonal and meridional wind observations are reproduced in the simulations, but the magnitude of the peak zonal wind around 140 km tends to be too small and the maximum meridional wind around 130 km is overestimated. The winds above 120 km altitude are found to be sensitive to changes in electric fields and ion densities, as was the case for the dawn side, but the effects of background winds and tides on the magnitudes of the winds above 120 km are found to be relatively small on the dusk side. The structure below 120 km appears to be related mainly to background winds and tides rather than auroral forcing, as was found in earlier studies on the dawn side, although the peak magnitudes of simulated wind variations in the 100 to 120 km altitude range are smaller than those observed. The source of the strong shears measured around I 10 km altitude on the dusk side is uncertain, but may be related to different kinds of oscillations, such as gravity waves, non migrating semidiurnal tides, or secondary oscillations produced by non linear interactions between waves.