The terminal structure of the unsteady boundary‐layer equations is investigated for the problem of impulsive flow past a circular cylinder. It is known that both the classical and interacting boundary‐layer equations for this problem are singular and the singular structure for the interacting boundary layer on a circular cylinder has not been properly resolved using the classical finite difference approach within an Eulerian framework. The objective of this paper is to resolve the singular structure for both the classical and interacting boundary layers for the impulsively started flow past a cylinder. An adaptive‐grid scheme, coupled to a panel method for the interacting case, is employed to resolve the extremely small time and length scales associated with a terminal structure defined by the emergence of a singularity. Calculations performed in an Eulerian coordinate system show that interacting boundary‐layer calculations terminate sooner than the classical boundary‐layer calculation, and as the Reynolds number decreases, the singularity occurs earlier in time and closer to the rear stagnation point of the circular cylinder. Comparisons with previous Lagrangian and fixed‐grid Eulerian results are discussed. ©1996 American Institute of Physics.