Abstract We use the EPIC general circulation model, described in the companion paper by Dowlinget al.(1998.Icarus132, 221–238), to simulate large vortices under conditions similar to those found on Neptune. The vortices are anticyclones with roughly elliptical cross sections and exhibit motions that resemble the behavior of Neptune's Great Dark Spot (GDS), including equatorward drift, oscillations in aspect ratio and orientation angle, and tail formation. The vortices also exhibit three-dimensional motions that may explain the occasional appearance of the GDS as two overlapping ellipses. We find that the meridional drift of the vortices is correlated with the meridional gradient of the background absolute vorticity, β*. This result complements studies of hurricane drift. The correlation suggests that the drift rate of GDS-type vortices on Neptune, which can be monitored over the long term by the Hubble Space Telescope (HST), is diagnostic of the vorticity gradient on the planet. The best fit to the Voyager GDS drift rate in our simulations corresponds to β* ≈ 2 × 10−12m−1s−1. This is about 1 3 of the value given by the zonal-wind profile determined by fitting an even polynomial in latitude to the cloud-tracking data (Sromovskyet al.1993). Refitting the data with spherical harmonics (Legendre polynomials) yields a value for β* that is about 1 2 of the Sromovskyet al.value, and more in line with our vortex-drift results. We show that vortex shape oscillations occur both in the case β* = 0, corresponding to the analytical model of Kida (1981), and for β* > 0. Interpreting the shape oscillations is more complicated than interpreting meridional drift because shape oscillations are sensitive to the distribution of vorticity in the vortex as well as in the environment. Rossby-wave dispersion strongly affects the model vortices that drift too close to the equator. The vortices disrupt before reaching the equator, dispersing into waves that propagate in both the southern and northern hemispheres over the course of a few weeks.