Multibody wave energy converters are composed of several bodies interconnected by joints. Two different formulations are adopted to describe the dynamics of multibody systems: the differential and algebraic equations (DAEs) formulation, and the ordinary differential equations (ODEs) formulation. While the number of variables required for the description of the dynamics of a multibody system is greater in the DAE formulation than in the ODE formulation, the ODE formulation involves an extra computational effort in order to describe the dynamics of the system with a smaller number of variables. In this paper, pseudo-spectral (PS) methods are applied in order to solve the dynamics of multibody wave energy converters using both DAE and ODE formulations. Apart from providing a solution to the dynamics of multibody systems, pseudo-spectral methods provide an accurate and efficient formulation for the control of multibody wave energy converters. As an application example, this paper focuses on the dynamic modeling of a three-body hinge-barge device, where wave-tank tests are carried out in order to validate the DAE and ODE models against experimental data. Comparison of the ODE and DAE PS methods against a reference model based on the straightforward (Runge-Kutta) integration of the equations of motion shows that pseudo-spectral methods are computationally more stable and require less computational effort for short time steps.