Static electric fields which vary around the major axis of a torus are shown to give rise to islands in the drift surfaces of the particles, with flutelike perturbations as the most dangerous ones. The size of the islands in the ion drift surfaces can be a sizable fraction of the plasma radius, while electron drift surface islands are smaller by the square root of the ratio of the Larmor radii. If a number of low-frequency waves of reasonably high azimuthal wave number is present in a tokamak discharge, a series of islands exists which can give rise to enhanced electron diffusion. Since the electric field does not appear static to the ions, they are not affected in a similar fashion. The enhanced electron diffusion due to island formation is compared with another mechanism of enhanced diffusion which was recently proposed by Pogutse.