The current-voltage (J-V) characteristics of ITO/polymer film/Al or Au structures of poly(phenylene vinylene) (PPV) and a dialkoxy PPV copolymer have been recorded for a range of different film thickness d and temperatures T. At high applied bias all the characteristics can be fitted over a given range to a power law J = KVm, where m increases with decreasing T, log(K) is proportional to m, and K is proportional to d-α m, where α∼2 (ITO/polymer film/Al devices) and ∼1 (ITO/polymer film/Au devices). Different single carrier space charge limited conduction theories have been used to try and explain this behavior. The analytical theory in which the carrier density is decreased by an exponential trap distribution lying below effectively isoelectronic transport states is in good agreement, but cannot explain the thickness dependence of the ITO/ polymer film/Au devices and can be criticized as being physically unreasonable. A numerical analysis in which the mobility has the field and temperature dependence found for hopping transport in disordered systems is also in good agreement, but can only fit a small range of J and cannot explain the magnitude of K, the temperature dependence of m or the abrupt change in slope in the J-V characteristics with increasing bias. Mixed models are equally good but cannot explain the deviations from experiment. We consider that further experimental studies of carrier mobilities and the nature of the traps present in such materials is required to distinguish between these models and resolve the nature of bulk limited conduction in conjugated polymers. © 1998 American Institute of Physics.