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In this paper, we present the dynamic modeling of a 3D-hybrid underwater eel-like robot using recursive algorithms based on the Newton-Euler equations. The robot is composed of a sequence of parallel modules connected in series. The algorithm gives the head accelerations and the joint torques as a function of the Cartesian positions, velocities and accelerations of the platform of the modules. The proposed algorithm can be considered as a generalization of the recursive Newton-Euler inverse dynamic algorithm of serial manipulators with fixed base. The proposed algorithm is easy to implement and to simulate whatever the number of degrees of freedom of the robot. An example with 12 parallel modules is presented.