This work addresses the multi-agent coordinated path following problem consisting of a class of underactuated vehicles capable of following a class of closed embedded curves in the three-dimensional space and proposes a solution using a nested set stabilization approach. The stabilization of the first set restricts each agent to the assigned path following manifold and ensures that each system stays on the path indefinitely when initialized in the neighbourhood of the path. Stabilizing the second set, contained inside the first, solves the position, velocity, acceleration, or jerk-related coordination constraints. The third set, contained in the second set, satisfies the yaw, or yaw-rate related coordination constraints. The reduction theorem establishes the asymptotic stability of the overall multi-agent system. Finally, in simulations, the proposed controller’s convergence on a multi-agent system consisting of three quadrotors is demonstrated.