Numerical simulations of a single magnetic island evolution are presented in the regime where the island width is smaller than an ion Larmor radius. It is shown that the island rotation is controlled by particle diffusion due to collisions or a background of microturbulence. As expected from the theory of a stationary island, there exist cases where linearly stable magnetic perturbation are nonlinearly self-sustained. This situation corresponds to large poloidal beta and temperature gradient. The drive is due to diamagnetic frequency effects. However, this situation is not generic, and islands can also decay. It is found that a magnetic island is self-sustained for a negative off-diagonal diffusion coefficient. This case occurs in a tokamak if the inward particle pinch is due to the temperature gradient. (author). 30 refs.