Kinesin and dynein are motor proteins that move in opposite directions along microtubules. In this study, we examine the consequences of having kinesin and dynein (ciliary outer arm or cytoplasmic) bound to glass surfaces interacting with the same microtubule in vitro. Although one might expect a balance of opposing forces to produce little or no net movement, we find instead that microtubules move unidirectionally for several microns (corresponding to hundreds of ATPase cycles by a motor) but continually switch between kinesin-directed and dynein-directed transport. The velocities in the plus-end (0.2-0.3 microns/s) and minus-end (3.5-4 microns/s) directions were approximately half those produced by kinesin (0.5 microns/s) and ciliary dynein (6.7 microns/s) alone, indicating that the motors not contributing to movement can interact with and impose a drag upon the microtubule. By comparing two dyneins with different duty ratios (percentage of time spent in a strongly bound state during the ATPase cycle) and varying the nucleotide conditions, we show that the microtubule attachment times of the two opposing motors as well as their relative numbers determine which motor predominates in this assay. Together, these findings are consistent with a model in which kinesin-induced movement of a microtubule induces a negative strain in attached dyneins which causes them to dissociate before entering a force-generating state (and vice versa); reversals in the direction of transport may require the temporary dissociation of the transporting motor from the microtubule. The bidirectional movements described here are also remarkably similar to the back-and-forth movements of chromosomes during mitosis and membrane vesicles in fibroblasts. These results suggest that the underlying mechanical properties of motor proteins, at least in part, may be responsible for reversals in microtubule-based transport observed in cells.