AbstractThis technical note is concerned with aeroelastic flutter problems: the analysis of aeroelastic systems undergoing airspeed-dependent dynamic instability. Existing continuation methods for parametric stability analysis are based on marching along an airspeed parameter until the flutter point is found—an approach that may waste computational effort on low-airspeed system behavior, before a flutter point is located and characterized. Here, we describe a pseudospectral continuation approach that instead marches outward from the system’s flutter points, from points of instability to points of increasing damping, allowing efficient characterization of the subcritical and supercritical behavior of the system. This approach ties together aeroelastic stability analysis and abstract linear algebra and, by reducing the sample space in which the analysis needs to take place, provides efficient methods for computing practical aeroelastic stability properties—for instance, flight envelopes based on maximum modal damping and the location of borderline-stable zones.