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This article addresses the challenge of adaptive neural‐based asynchronous control for nonhomogeneous Markov jumping systems with input dead zones. Time‐varying transition probabilities are precisely characterized using a two‐layer nonhomogeneous Markov process. A hidden Markov model is employed to detect system modes and resolve the asynchronous issues of controllers. Based on the detected modes and a neural network strategy, an adaptive asynchronous control strategy is proposed. The Lyapunov stability theory is used to prove that the system remains probabilistically bounded under this control law. Finally, the effectiveness of the control strategy is demonstrated through a simulation example. [ABSTRACT FROM AUTHOR]