Rigid body molecular models possess symplectic structure and time-reversal symmetry. Standard numerical integration methods destroy both properties, introducing nonphysical dynamical behavior such as numerically induced dissipative states and drift in the energy during long term simulations. This article describes the construction, implementation, and practical application of fast explicit symplectic-reversible integrators for multiple rigid body molecular simulations, These methods use a reduction to Euler equations for the free rigid body, together with a symplectic splitting technique. In every time step, the orientational dynamics of each rigid body is integrated by a sequence of planar rotations. Besides preserving the symplectic and reversible structures of the flow, this scheme accurately conserves the total angular momentum of a system of interacting rigid bodies. Excellent energy conservation fan be obtained relative to traditional methods, especially in long-time simulations. The method is implemented in a research code, ORIENT and compared with a quaternion/extrapolation scheme for the TIP4P model of water. Our experiments show that the symplectic-reversible scheme is far superior to the more traditional quaternion method. (C) 1997 American Institute of Physics.