Passive energy dissipation systems have been identified as one of the modern structural protective systems against seismic disturbances. Research and development activities are on globally to develop appropriate design procedures and suitable technology for application in the field. Structural systems with energy-dissipating devices call for rigorous nonlinear analysis, which is a complex one and the results are highly sensitive to the type of input motion and component behavior assumed in the analysis. The Federal Emergency Management Agency 273 (FEMA 273) (1997) has suggested simplified procedures for replacing the original nonlinear system by an equivalent linear system. Recently, artificial intelligence (AI) techniques based on artificial neural networks (ANN) have been profitably used for solving complex problems of an iterative nature. Combining the equivalent model with an appropriate AI technique would help one to quickly predict the dynamic response of such yielding systems. This article highlights the feed forward back-propagation neural network using the Levenberg-Marquardt algorithm for predicting the response quantity of systems with energy-dissipating devices. The neural network is trained to reflect the nonlinear relationship of strength, stiffness, and damping existing in the system. The methodology developed is illustrated and validated with a chosen example from the FEMA 274 and is found to predict well the average peak displacement, base shear, and roof displacement. Based on these, the sensitivity studies have been carried out and the influence of each parameter on the results have been brought out. It may be noted that sensitivity details and the influence of each parameter do not show up in the regular time-series analysis. The main advantage of the methodology and the network developed is in quick preliminary decision on the amount and the number of dampers required to reduce peak displacement for a new design as well as for retrofitting.