The paper deals with the security control stabilization problem of uncertain Markov jump power systems with input dead zone under stochastic denial-of-service (DoS) attack. DoS attack is modeled as a discrete-time Markov process. Dual hidden Markov models are respectively used to detect the modes of the original power systems and the one under DoS attack. Based on the detected modes and neural networks (NNs), adaptive NN-based security asynchronous control strategies are proposed, where both state feedback and output feedback are studied simultaneously. With the developed control laws, all trajectories of the closed-loop systems are bounded stable in the stochastic setting. Simulation results demonstrate the correctness and usefulness of the proposed techniques.