This paper addresses the problem of coordinated motion control of underactuated autonomous underwater vehicles (AUVs) in three-dimensional (3D) oceanic environments. A nonlinear coordinated path following controller is designed to give an illustrative paradigm driving two underactuated AUVs along prior-planned parallel paths in 3D space based on Lyapunov theory, backstepping technique and invariant manifold principle, where one vehicle acts as a leader and the other is as follower. The key idea is to adapt the speed of the follower based on the single-variant “along-path parameter” information passed by the leader vehicle, such that the exchanged information is kept at a minimum compared to the posture and speed, or relative distance and orientation information of the leader required in most coordinated motion control cases. Simulation results show the performance of coordinated motion controller proposed for underactuated AUVs in 3D space.