A new method for calculating rate constants for fast reactions between two diatomic molecules is presented. The method involves applying a rotationally adiabatic capture theory with a simultaneous treatment of the rotational motions of both molecules. Results from calculations for dipole–dipole (SO + OH) and dipole–quadrupole (CN + O₂) interactions are compared with those obtained using more approximate methods based on various sudden approximations. Analytical formulae are derived for the rate constants in the limit of zero temperature, by using perturbation theory, and for high temperature, by using the infinite-order-sudden approximation. The importance of dispersion terms in the potential is also examined. An interesting prediction is that the rate constant for the fast reaction between two dipolar molecules is zero at temperature T= 0, increases as T^1/6 to a maximum at a very low temperature (typically close to 10 K) and then decreases, eventually having a temperature dependence of T^–1/6.