Multi-body wave energy converters are composed of several bodies interconnected by joints. Two different formulations are adopted to describe the dynamics of multi-body 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 multi-body 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 methods are applied in order to solve the dynamics of multi-body wave energy converters using both DAE and ODE formulations. Apart from providing a solution to the dynamics of multi-body systems, pseudo-spectral methods provide an accurate and efficient formulation for the control of multi-body wave energy converters. As an application example, this paper focuses on the dynamic modeling of a twobody hinge-barge device. Wave-tank tests were carried out on the device in order to validate the DAE and ODE formulation against experimental data. The comparison between pseudospectral methods and a method based on the integration of the equations of motion, e.g. the Runge-Kutta method, showed that pseudo-spectral methods are computationally more stable and they require a less computational effort for short time steps.