The results of simulation of microdischarges in a dielectric-barrier discharge are presented. These simulations have been carried out in two dimensions with an adaptive grid. The results presented are for oxygen at atmospheric pressure. The dielectric has little effect on the propagation of the streamerlike discharge until the very last stage. The dielectric capacitance has been found to have very little effect on the radical production efficiency. (C) 1997 American Institute of Physics. [S0021-8979(97)07621-4].