We report measurements and modeling studies of organic light-emitting diodes (LED's) with mobile ions incorporated into the active polymer layer, similar in structure to the light-emitting electrochemical cells (LEC's) reported by Pei el al. We show that movement of the ions, rather than electrons or holes, is responsible for the Ohmic electrode-polymer contacts observed in these devices. We show that for typical devices with polymer film thicknesses of 1000-2000 Angstrom, concentrations of ions greater than 10(20) cm(-3) are required for efficient electroluminescent behavior. We show also that under steady-state operation, the electric field is very low in the bulk of the polymer, and that the electron and hole currents are therefore driven mainly by diffusion. Quantitative modeling of electron-hole recombination matches observed emission profiles.