The current-voltage relationships in organic electroluminesent devices are derived for the following two cases: (i) double-carrier injection trap-charge Limited (TCL) regime, and (ii) TCL conduction with internal photodetrapping. Several experimental observations are explained based on our equations. Location of the recombination zone is predicted. A numerical model is also developed to simulate the TCL conduction. Current-voltage characteristics, band and charge profiles are obtained to elucidate the conduction mechanisms in the organic electroluminescent devices with large trap densities.