The traditional linearized stellar-structure equations, which provide information on the global stability of a stellar equilibrium state, are shown to engender a class of continuous modes, if the eigenfunctions are sought in a generalized function space. To endow the intuitive concept of ‘Local Stellar Statility’ with a precise mathematical meaning, we endeavour to link this notion to the family of continuous spectra. We indicate a simple numerical method to compute the eigenfunctions associated with these modes, and we illustrate our approach by briefly analysing the continuous spectra connected with the radial and nonradial dynamical stability problem.