Motor-driven bidirectional transport inside a cell is an intriguing phenomenon where multiple dyneins and kinesins drag cargoes and deliver them to specific locations. Quite often, both anterograde (plus) and retrograde (minus) directed motors reside simultaneously on the cargo and co-ordinate their activity such that the motion of the cargo looks like spells of plus directed and minus directed segments, with pauses in between. The stochastic tug-of-war model is widely used to analyze this motion, largely studied by computer simulations. Here, we present some analytical results for this model, such as the average durations of plus and minus-run segments and tug-of-war events as well as probabilities of persistence and reversal of directions following a tug-of-war. We show that cargo motion has memory in case of 2 dyneins and 1 kinesin driving together, while it is absent when only a dynein and a kinesin is involved. © 2013 American Institute of Physics.