Artificial neural networks (ANN) have recently emerged as a powerful computer-aided design (CAD) tool for modeling nonlinear devices and circuits. The overall objective of this thesis is to develop sensitivity analysis based neural network techniques for both frequency domain and transient modeling of nonlinear circuits. The proposed techniques not only add sensitivity data to the obtained model but also make conventional training more efficient. The first contribution of this thesis is the development of sensitivity-analysis-based adjoint neural-network (SAANN) technique for modeling microwave passive components. This method adds sensitivity data to the obtained model. In addition, the SAANN technique reduces the amount of training data required for model development increasing the efficiency of model development. As a further contribution, this thesis presents a novel robust modeling technique, adjoint state-space dynamic neural network (ASSDNN), for transient modeling of nonlinear optical/electrical components and circuits. This technique adds time-domain sensitivity data, which does not exist in current optoelectronic and physics-based simulators, to the output of the obtained model. The proposed technique requires less training data for creating the model and consequently makes training faster and more efficient. Furthermore, this technique was developed such that it can take advantage of parallel computation. This results in the technique being much faster and more efficient than conventional transient modeling techniques. In addition, the evaluation time for models of nonlinear optical-electrical and physics-based devices generated using the proposed technique is reduced compared to current simulation tools.