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Abstract This paper introduces Deep Recurrent Neural Network (DRNN) structure for time-domain modeling of nonlinear circuits. DRNN can be directly trained by sampled input-output waveforms of the original nonlinear circuit without knowing the internal details of the circuit. A training algorithm based on Real-Time Recurrent Learning (RTRL) is developed to train the proposed DRNN. After the training phase, DRNN provides accurate and fast macromodel of the nonlinear circuit. Our experimental results show that DRNN extends the ability of conventional neural-based models to express the dynamic behavior of a nonlinear circuit, and also significantly enhances the accuracy of the conventional neural circuit modeling. Moreover, DRNN is considerately faster than the existing models in simulation tools. The validity and advantages of the proposed deep learning-based method are verified by time-domain modeling of three nonlinear devices including 5-stage CMOS receiver, commercial TI's LM324 power amplifier, and TI's SN74AHCT540 device. [ABSTRACT FROM AUTHOR]