Derivation of formulas relating leaf speeds and beam dose rates for delivering planned intensity profiles to static and moving targets in dynamic multileaf collimator (DMLC) intensity modulated radiation therapy (IMRT) is presented. The analysis of equations determining algorithms for DMLC IMRT delivery under a variable beam dose rate reveals a multitude of possible delivery strategies for a given intensity map and for any given target motion patterns. From among all equivalent delivery strategies for DMLC IMRT treatments specific subclasses of strategies can be selected to provide deliveries that are particularly suitable for clinical applications providing existing delivery devices are used. Special attention is devoted to the subclass of beam dose rate variable DMLC delivery strategies to moving body anatomy that generalize existing techniques of such deliveries in Varian DMLC irradiation methodology to static body anatomy. Few examples of deliveries from this subclass of DMLC IMRT irradiations are investigated to illustrate the principle and show practical benefits of proposed techniques.