There are two main difficulties for identification of dual-rate sampled nonlinear systems; one is the unknown nonlinear properties and the other is the dual-rate sampled data. Considering the above two points, this paper proposes a cycle reservoir with regular jumps (CRJ) network based recursive identification algorithm. Unlike a traditional method, the proposed one does not require a priori knowledge of the nonlinearity and can handle dual-rate data; therefore, its applicability can be guaranteed. Firstly, the CRJ network is used to describe the nonlinear characteristics of the target systems. However, the update of the CRJ network requires the missing outputs, thus the auxiliary model identification theory is adopted and the missing outputs are replaced by the estimated outputs of the network. In this process, the output weights of the CRJ network are updated at a slow rate, while the estimates of the missing outputs are updated quickly, resulting in an interactive estimation computation process. Then, to improve the identification accuracy, the hyper-parameters of the CRJ network are optimized by means of the particle swarm optimization algorithm. Finally, simulation examples are presented to demonstrate the effectiveness of the proposed algorithm.