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Abstract The authors investigate predictor control for the cascaded system of a non‐linear ordinary differential equation with counter‐convecting transport partial differential equations with propagation velocities dependent on partial differential equations states in this paper. Stability analysis of the closed‐loop system is shown by using the infinite‐dimensional backstepping transformations and an appropriate Lyapunov functional. A predictor control is developed such that the closed‐loop system is asymptotically stable. An example is given to illustrate the validity of the proposed method.