Despite narrow bands and large energy gaps, which result in a negligible number of intrinsic carriers, high-quality molecular crystals, such as pentacene and naphthalene, show high mobilities at low temperatures. As a result, injected carriers can have their "temperature" increased by easily attainable electric fields. Their mobility is then expected to decrease with an increasing field, both because of the increased scattering rate and the increase in the effective mass due to the nonparabolicity of the energy bands. Using Poisson's equation, we investigate the effect on the current voltage characteristic of the mobility decrease being so steep over some field range that the drift velocity (v(d)) decreases with an increasing field; that is, the sample displays negative differential mobility (NDM) over that range. NDM is expected for samples in which the effective mass increases. We find that, with increasing voltage, V, after the Ohm's law region, there is a region in which J proportional to V-2, as expected for a space-charge-limited value of J. When V is large enough to cause heating of the carriers, J increases less rapidly than V, tending toward a linear dependence on V in the hot carrier region. Thus, V/J tends to saturate at high fields. It is shown that the data of Schon et al. for pentacene, when properly interpreted, show saturation of V/J rather than that of v(d), as they claimed. The direct measurement of v, versus the field by the time-of-flight method for naphthalene at low temperatures by Warta and Karl was interpreted by them as indicating saturation of v(d). We point out that the determination of v(d) by the time-of-flight method in a situation with varying mass and trapping is not straightforward. (C)0 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2595-2600, 2003