The dynamics of stiff polymers in the liquid or liquid-crystalline state is usually described by the rigid rod model. To account, at least to a first approximation, for the partial flexibility of the actual chain, the slightly-bending-rod model has been recently proposed, and a simplified two-dimensional version of the model has been developed in some detail. In this paper, we consider the full three-dimensional dynamic equation which, in its general form, is too complex for predictive purposes. We then derive a reduced form of the dynamic equation on the basis of the fact that some of the configurational variables have a much faster dynamics than others. The mathematical structure of the reduced form, though still complex, is close enough to that of the rigid rod model to allow for predictive calculations.