Purpose <p>Aero-engine dual rotor systems are typically subjected to various base motion excitations induced by the maneuvering flight of aircrafts. The base motion frequency is usually significantly lower than shaft rotating frequency, and the ratio of the latter to the former ranges from 10² to 10⁴ in engineering practice. This low-frequency excitation problem corresponds to the long-period solution, whose computation can entail high costs and pose challenges to efficient vibration analysis, especially for the large-scale systems. This work aims to develop an efficient numerical algorithm to address these low-frequency excitation problems.</p> Methodology <p>A double-level parallel numerical continuation method integrating multiple shooting method and component mode synthesis is proposed to analyze the periodic vibration of dual-rotor systems subjected to low-frequency base excitations. Two solution schemes are adopted to evaluate the computational efficiency of the parallel numerical algorithm.</p> Conclusion <p>The computational efficiency of both single- and continuous-solution modes for parallel numerical method is analyzed; and the optimal parameter configuration strategy for each mode is provided. There exists a V-shaped curve between running time and the number of threads in the single-solution mode of the parallel algorithm. The double-level parallel numerical algorithm presented a superior maximal speed-up ratio compared to its single-level counterpart for continuous-solution mode. In addition, the influence of maneuvering flight frequency on rotor vibration characteristics is investigated. It is revealed that maneuvering flight frequency primarily affects the nonlinear characteristics of the rotor by altering the asymmetric support stiffness of rolling bearings.</p>