This paper is concerned with deducing the most important features of the steady separated flow past a circular cylinder in the limit of vanishing viscosity. First of all, it is shown that the experimental results reported in an earlier article cannot be reconciled with the notion that, as the Reynolds number Re is increased, the flow becomes inviscid everywhere and that viscous effects remain confined within infinitesimally thin shear layers. In contrast, the limiting solution is visualized as exhibiting three essential features: a viscous, closed ‘wake bubble’ of finite width but with a length increasing linearly with Re in which inertial and viscous effects are everywhere of equal order of magnitude; an outer inviscid flow; and, separating the two regions, a diffuse viscous layer covering large sections of the external field. Further properties of this asymptotic solution include: a finite form drag, a negative rear pressure coefficient at the rear stagnation point of the cylinder, and a Nusselt number for heat transfer which becomes independent of Re along the non-wetted portion of the cylinder surface. This model is shown to be consistent with all the experimental data presently available, including some new heat transfer results that are presented in this paper.An approximate technique is also proposed which takes into account the asymptotic character of the flow in the vicinity of the cylinder and which predicts the pressure distribution around the cylinder in good agreement with the experiments.