A hybrid seismic analysis computing the full nonlinear response of building structures is proposed and validated in this paper. Recurrent neural networks are trained to predict the nonlinear hysteretic response of isolation devices with deformation- and velocity-dependent behavior. Then, they are implemented in an explicit time integration method for time history analysis. A comprehensive framework is proposed to develop and test deep learning models considering the data framing, the network architecture, and the learning behavior. Hybrid seismic analyses of three base-isolated building models subjected to four ground motions with different properties were performed in order to check their efficiency. The small relative errors of computed results to those of the conventional analysis successfully validate the accuracy of the proposed analysis. Its computation time depends mainly on the ground motion duration and is considered negligible. The development of the machine learning model is more time-consuming but nonrepetitive since it can be saved and reused to analyze any new structure containing the same target components. The proposed hybrid seismic analysis overcomes the shortcomings of usual applications of machine learning in structural response prediction problems being limited to specific response quantity(s) of the same structure(s) used at the training process. By taking advantage of both mechanics-based and data-driven methods, results reveal that hybrid analysis is an efficient tool for building-response simulation.