According to the "stop-and-go" hypothesis of slow axonal transport, cytoskeletal and cytosolic proteins are transported along axons at fast rates but the average velocity is slow because the movements are infrequent and bidirectional. To test whether this hypothesis can explain the kinetics of slow axonal transport in vivo, we have developed a stochastic model of neurofilament transport in axons. We propose that neurofilaments move in both anterograde and retrograde directions along cytoskeletal tracks, alternating between short bouts of rapid movement and short "on-track" pauses, and that they can also temporarily disengage from these tracks, resulting in more prolonged "off-track" pauses. We derive the kinetic parameters of the model from a detailed analysis of the moving and pausing behavior of single neurofilaments in axons of cultured neurons. We show that the model can match the shape, velocity, and spreading of the neurofilament transport waves obtained by radioisotopic pulse labeling in vivo. The model predicts that axonal neurofilaments spend approximately 8% of their time on track and approximately 97% of their time pausing during their journey along the axon.