A closed set of equations relating the macroscopic variables are derived from the linearized kinetic equations with a Bhatnagar‐Gross‐Krook collision term. The collisional fluid limit of these expressions are in complete agreement with the most exact magnetohydromagnetic equations, including viscosity. The collisionless fluid limit provides an extension of the Chew‐Goldberger‐Low equations, now valid when the diamagnetic velocity is comparable to the electric drift. The generalized equations may be used to investigate the transition between the weakly collisional condition, where resonant particle effects are important, and the strongly collisional condition where viscosity becomes dominant.