We study numerically the motion of vortices in nonequilibrium Bose-Einstein condensates, that are described by a generalized Gross-Pitaevskii equation. We analyze how the vortex properties are modified when moving away under deviation from equilibrium. We find that far from equilibrium, the radial component dominates over the azimuthal one in the distribution of vortex currents at large distances from the vortex core. The modification of the current pattern has a strong effect on the vortex-antivortex interaction energy, that can become entirely repulsive. The vortex trajectories are also strongly affected by the driving and dissipation. Self acceleration of vortices is observed in the strong nonequilibrium case.