Abstract A model of fast axonal transport of organelles that accounts for dynein transport in an inactive state toward the axonal synapse is developed. It is assumed that anterograde transport of inactive dynein in an axon is powered by kinesin motors. It is further assumed that the probability of organelle attachment to a dynein motor is directly proportional to the concentration of free dynein motors available at a particular location in the axon. The results predicted by two models (the first one is that which incorporates dynein transport and the second one is the traditional model that does not incorporate dynein transport) are compared. The obtained results suggest that the availability of dynein motors in a particular location in an axon can be a factor limiting fast axonal transport.