The relativistic velocity composition paradox of Mocanu and its resolution are presented. The paradox, which rests on the bizarre and counterintuitive non-communtativity of the relativistic velocity composition operation, when applied to noncollinear admissible velocities, led Mocanu to claim that there are “some difficulties within the framework of relativistic electrodynamics.” The paradox is resolved in this article by means of the Thomas rotation, shedding light on the role played by composite velocities in special relativity, as opposed to the role they play (...) in Galilean relativity. (shrink)