This paper proposes an alternative numerical method to compute the overall response of nonlinear composites with complex microstructures, based on Fourier series. The method avoids meshing and directly uses microstructure images, making it suitable for a wide range of microstructures. It begins with the case of elastic nonhomogeneous constituents, where an iterative procedure is proposed to solve the Lippman-Schwinger equation. The method is then extended to nonlinear constituents through a step-by-step integration in time. The accuracy of the method is assessed by varying the spatial resolution of the microstructures. The numerical algorithm is detailed, including continuous and discrete formulations, and the influence of spatial resolution on the accuracy is discussed. The method is applied to composites with "random" microstructures, and the results are compared with analytical solutions for laminates and circular fibers. The study also investigates the influence of fiber arrangement on the local and overall responses of nonlinear composites, considering both regular and random configurations. The results highlight the importance of spatial resolution and fiber arrangement in predicting the effective properties of the composites.This paper proposes an alternative numerical method to compute the overall response of nonlinear composites with complex microstructures, based on Fourier series. The method avoids meshing and directly uses microstructure images, making it suitable for a wide range of microstructures. It begins with the case of elastic nonhomogeneous constituents, where an iterative procedure is proposed to solve the Lippman-Schwinger equation. The method is then extended to nonlinear constituents through a step-by-step integration in time. The accuracy of the method is assessed by varying the spatial resolution of the microstructures. The numerical algorithm is detailed, including continuous and discrete formulations, and the influence of spatial resolution on the accuracy is discussed. The method is applied to composites with "random" microstructures, and the results are compared with analytical solutions for laminates and circular fibers. The study also investigates the influence of fiber arrangement on the local and overall responses of nonlinear composites, considering both regular and random configurations. The results highlight the importance of spatial resolution and fiber arrangement in predicting the effective properties of the composites.