Stability of linear systems with several very small as well as several very large parasitic parameters is analyzed. Time-scale separation is used in conjunction with the recently introduced notion of strong D-stability to prove general asymptotic stability results for this class of systems. Moreover, it is observed that, contrary to the case studied by Desoer and Shensa (1970) which involved a single small parasitic parameter and a single large parasitic parameter, the system cannot be transformed into a standard multiparameter singular perturbation problem. Hence, systems containing both stray and sluggish elements do indeed represent a separate class of problems in asymptotic analysis.