A novel real-time recurrent neural network (RTRNN) approach is presented for dynamic behavioral macromodeling of nonlinear microwave devices. A modified real-time recurrent learning algorithm is developed to train the neural network model. This proposed RTRNN model can directly be developed from input-output waveform data without having to rely on the internal details of the devices. Once trained, this model provides fast and accurate prediction on the analog behaviors of the nonlinear microwave devices under modeling, which can readily be incorporated into high-level circuit simulation and optimization. This RTRNN approach enhances the neural modeling speed and accuracy. Moreover, it also provides additional flexibility in handing diverse needs of nonlinear microwave circuit designs in the time domain, such as single-tone and multiple-tone simulations and large-signal simulations by comparison to the previously published neural models. The validity of this proposed approach is illustrated through behavioral macromodeling of two typical microwave devices: power amplifiers and pHEMTs.