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In the computer-aided design (CAD) area, the recurrent neural network (RNN) has shown notable functionality in generating fast and high-performance models rather than the models in simulation tools. Predicting time sequences is a pervasive and challenging problem that may require identifying the dependencies between sequences that RNN is capable of performing. Despite all its features, conventional RNN still faces challenges such as limited accuracy and a large number of parameters. Therefore, we propose new macromodeling methods for nonlinear circuits called the Clockwork-RNN (CWRNN) and its hybrid version which is a more powerful but simpler implementation of a conventional RNN architecture with relatively little model complexity. In addition, CWRNN inherently models complex dependencies without the need for a large number of parameters. As a result, the computational cost is less than conventional RNN. Moreover, understanding and implementing the CWRNN is relatively simple and provides great flexibility in architectural configuration by introducing modules with several clock rates of exponents of 2. In addition to the above new modeling technique, we proposed the Hybrid-Module CWRNN as another new modeling method that utilizes modules of various exponents of different numbers resulting in further accuracy improvement of the CWRNN. Furthermore, the models obtained from the proposed techniques required much smaller simulation times compared to the current models used in simulation tools. Three nonlinear high-frequency examples have been utilized to verify the benefits of the proposed modeling methods.