The onset of initial instability in a developing Couette flow following the impulsive starting of an inner rotating cylinder is analyzed using linear theory. It is well known that there is a critical Taylor number Ta-c at which Taylor vortices first appear between two concentric cylinders. For Ta > Ta-c Taylor-like vortices occur at a certain elapsed time. In the present study, the critical time t(c) to represent the onset of this initiating instability, which then grows as toroidal vortices, is analyzed using propagation theory. For this purpose a self-similar transformation is forced through scaling analysis. The resulting stability criteria compare well with the available experimental data for vortices in water. The new measures represent the onset of the fastest growing instability and also suggest the detection time for the manifestation of secondary flow in the primary time-dependent Couette flow. (C) 2004 Elsevier Ltd. All rights reserved.