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A recursive filtering method for nonlinear Markov jump systems with one-step randomly delayed observations has been proposed. The developed method is based on the linearization of the system and observation functions at specific points at each time step, and then the multiple-integration in the filtering process can be solved. To grantee moderate computational load of the algorithm, the estimates under respective modes at previous time instant are mixed. Furthermore, the observations are utilized to update the prior probabilities of random time delays, then the conditional means and covariances of residual errors can be calculated to obtain the overall estimates. Simulation results are given to demonstrate the validity of this method in handling with the state estimation problem for the nonlinear Markov jump systems with one-step randomly delayed observations.