The cooperative path following problem of multiple underactuated autonomous underwater vehicles (AUVs) involves two tasks. The first one is to force each AUV to converge to the desired parameterized path. The second one is to satisfy the requirement of a cooperative behavior along the paths. In this paper, both of the tasks have been further studied. For the first one, a simplified path following controller is proposed by incorporating the dynamic surface control (DSC) technique to avoid the calculation of derivatives of virtual control signals. Besides, in order to handle the uncertain dynamics, a new type of neural network (NN) adaptive controller is derived, and then an NN based energy efficient path following controller is firstly proposed, which consists of an adaptive neural controller dominating in the neural active region and an extra robust controller working outside the neural active region. For the second one, in order to reduce the amount of communications between multiple AUVs, a distributed estimator for the reference common speed is firstly proposed as determined by the communications topology adopted, which means the global knowledge of the reference speed is relaxed for the problem of cooperative path following. The overall algorithm ensures that all the signals in the closed-loop system are globally uniformly ultimately bounded (GUUB) and the output of the system converges to a small neighborhood of the reference trajectory by properly choosing the design parameters. Simulation results validate the performance and robustness of the proposed strategy.