  We generalize the theory of underlying one-step methods to strictly stable
general linear methods (GLMs) solving nonautonomous ordinary differential
equations (ODEs) that satisfy a global Lipschitz condition. We combine this
theory with the Lyapunov and Sacker-Sell spectral stability theory for one-step
methods developed in [34,35,36] to analyze the stability of a strictly stable
GLM solving a nonautonomous linear ODE. These results are applied to develop a
stability diagnostic for the solution of nonautonomous linear ODEs by strictly
stable GLMs.
