Abstract: In order to address the diverse requirements of linear systems and their local nonlinearity with respect to time steps, a trade-off between the accuracy and efficiency is necessary for the dynamic response analysis of systems with local nonlinearity. This method introduces a heterogeneous time step coupling algorithm for efficiently calculating the dynamic response of local nonlinear systems. Initially, a step-by-step integral equation for acceleration increment is formulated by the grounds of a heterogeneous time step and of a numerical integration scheme for linear and local nonlinear components. Subsequently, the transmission of nonlinear forces and system responses between the linear and nonlinear parts enables the step-by-step solution of the system response and nonlinear force. Finally, a spring-oscillator system and a large-scale steel frame structure are analyzed by using the proposed approach, and dynamic responses are compared with those of the Newmark-Newton and of ODE methods. The analysis results demonstrate that the method proposed can effectively and accurately compute dynamic responses.