Simple and efficient way of integrating rigid rotations is presented. The algorithm is stable, second-order accurate, and in its explicit version involves evaluation of only two exponential maps per time step. The semi-explicit version of the proposed scheme improves upon the long-term stability, while it retains the explicitness in the force evaluation. The algebraic structure of both schemes makes them suitable forthe analysis of constrained multi-body systems. The explicit algorithm is specifically aimed at the analysis involving small incremental rotations, where its modest computational cost becomes the major advantage. The semi-explicit scheme naturally broadens the scope of possible applications. Copyright © 2009 John Wiley & Sons, Ltd.