This paper addresses the cooperative path following the problem of ring-networked under-actuated autonomous surface vehicles on a closed curve. A cooperative guidance law is proposed at the kinematic level such that a symmetric formation pattern is achieved. Specifically, individual guidance laws of surge speed and angular rate are developed by using a backstepping technique and a line-of-sight guidance method. Then, a coordination design is proposed to update the path variables under a ring-networked topology. The equilibrium point of the closed-loop system has been proven to be globally asymptotically stable. The result is extended to the cooperative path following the lack of sharing of a global reference velocity, and a distributed observer is designed to recover the reference velocity to each vehicle. Moreover, the cooperative path following the presence of an unknown sideslip is considered, and an extended state observer is developed to compensate for the effect of the unknown sideslip. Both simulation and experimental results are provided to illustrate the effectiveness of the proposed cooperative guidance law for the path following over a closed curve.