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Abstract In this paper, a new technique is presented for parametrically studying the steady-state dynamics of piecewise-linear nonsmooth oscillators. This new method can be used as an efficient computational tool for analyzing the nonlinear behavior of dynamic systems with piecewise-linear nonlinearity. The new technique modifies and generalizes the bilinear amplitude approximation method, which was created for analyzing proportionally damped structural systems, to more general systems governed by state-space models; thus, the applicability of the method is expanded to many engineering disciplines. The new method utilizes the analytical solutions of the linear subsystems of the nonsmooth oscillators and uses a numerical optimization tool to construct the nonlinear periodic response of the oscillators. The method is validated both numerically and experimentally in this work. The proposed computational framework is demonstrated on a mechanical oscillator with contacting elements and an analog circuit with nonlinear resistance to show its broad applicability.