As an evolutional concept of variable cycle engine, the adaptive cycle engine draws widely attention with high expectations. It combines a variable geometry schedule and component matching principles to demonstrate its advantages such as avoiding severe inlet spillage drag and the wide variable cycle characteristics. Thus, this paper aims at equilibrium running principle analysis on an adaptive cycle engine at variable operating modes, deriving the equilibrium running equations of an adaptive cycle engine for the first time, and exploring the physical essence of components matching principle on the basis of a newly developed nonlinear component-based adaptive cycle engine performance model. It uncovers the physical essence of components matching relationships and provides mathematical derivation of equilibrium running principles which lay theoretical foundation of the variable geometries modulation schedule and overall performance optimization on an adaptive cycle engine.@en