In this article, a recurrent neural network (RNN) method is employed for dynamic time-domain modeling of both linear and nonlinear microwave circuits. An automated RNN modeling technique is proposed to efficiently determine the training waveform distribution and internal RNN structure during the offline training process. This technique extends a recent automatic model generation (AMG) algorithm from frequency-domain model generation to dynamic time-domain model generation. Two types of applications of the algorithm are presented, transient electromagnetic (EM) behavior modeling of microwave structures, and time-domain envelope modeling of power amplifiers (PA). For transient EM modeling, we consider EM structures with varying material and geometrical parameters. AMG automatically varies the EM structural parameters during training and drives time-domain EM simulators to generate necessary amount of data for RNN to learn. AMG aims to model the transient behavior with minimum RNN order while satisfying accuracy requirements. In modeling PA behavior, an envelope formulation is used to specifically learn the AM/AM and AM/PM distortions due to third-generation (3G) digital modulation input. The RNN PA model is able to model these time domain distortions after training and can accurately model the amplifier behavior in both time (AM/AM, AM/PM) and frequency (spectral re-growth). V