AbstractThis paper studies combat between two homogeneous forces modelled with variable‐coefficient Lanchester‐type equations of modern warfare with supporting fires not subject to attrition. It shows that this linear differential‐equation model for combat with supporting fires may be transformed into one without the supporting fires so that all the previous results for variable‐coefficient Lanchester‐type equations of modern warfare (without supporting fires) may be invoked. Consequently, new important results for representing the solution (i.e. force levels as functions of time) in terms of canonical Lanchester functions and also for predicting force annihilation are developed for this model with supporting fires. Important insights into the dynamics of combat between two homogeneous forces with such supporting fires are