For certain p-n junctions, it has been observed that the measured current-voltage characteristics deviate from the ideal case of the diffusion model. It is the purpose of this paper to show that the current due to generation and recombination of carriers from generation-recombination centers in the space charge region of a p-n junction accounts for the observed characteristics. This phenomenon dominates in semiconductors with large energy gap, low lifetimes, and low resistivity. This model not only accounts for the nonsaturable reverse current, but also predicts an apparent exp (qV/nkT) dependence of the forward current in a p-n junction. The relative importance of the diffusion current outside the space charge layer and the recombination current inside the space charge layer also explains the increase of the emitter efficiency of silicon transistors with emitter current. A correlation of the theory with experiment indicates that the energy level of the centers is a few kT from the intrinsic Fermi level.