In this paper, we investigate the linear and nonlinear response of shape memory alloy (SMA)-based Duffing and quadratic oscillator under large deflection conditions. In this study, we first present thermomechanical constitutive modeling of SMA with a single degree-of-freedom system. Subsequently, we solve equation to obtain linear frequency and nonlinear frequency response using the method of harmonic balance and validate it with numerical solution as well as averaging method under the isothermal condition. However, for nonisothermal condition, we analyze the influence of cubic and quadratic nonlinearity on nonlinear response based on method of harmonic balance. Analysis of results leads to various ways of controlling the nature and extent of nonlinear response of SMA-based oscillators. Such findings can be effectively used to control external vibration of different systems. © Copyright 2018 by ASME.