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Next-generation aircraft designs often incorporate multiple large propellers attached along the wingspan (distributed electric propulsion), leading to highly flexible dynamic systems that can exhibit aeroelastic instabilities. This paper introduces a validated methodology to investigate the aeroelastic instabilities of wing–propeller systems and to understand the dynamic mechanism leading to wing and whirl flutter and transition from one to the other. Factors such as nacelle positions along the wing span and chord and its propulsion system mounting stiffness are considered. Additionally, preliminary design guidelines are proposed for flutter-free wing–propeller systems applicable to novel aircraft designs. The study demonstrates how the critical speed of the wing–propeller systems is influenced by the mounting stiffness and propeller position. Weak mounting stiffnesses result in whirl flutter, while hard mounting stiffnesses lead to wing flutter. For the latter, the position of the propeller along the wing span may change the wing mode shapes and thus the flutter mechanism. Propeller positions closer to the wing tip enhance stability, but pusher configurations are more critical due to the mass distribution behind the elastic axis.