A biglobal stability approach formulated as an initial value problem is used to study the occurrence of biglobal modes for the flow around a NACA0015 airfoil at a high angle of attack. For the stability analysis of the NACA0015 airfoil both steady and unsteady base flows are considered. An important focus of the paper is on elaborating the differences between the stability characteristics of steady and unsteady base flows. The connection between experimentally observed spanwise periodically occurring three-dimensional separated regions (also referred to as stall cells when occurring on aircraft wings at high angles of attack) and unstable biglobal modes is explored. The occurrence of these three-dimensional separated flow regions can have a detrimental effect on the controllability of the airplane at deep stall conditions. In this paper results from direct numerical simulations of the flow past a NACA0015 airfoil at angle of attack, α = 18°, and Re = 1, 000 are presented. The relevance of the linearly unstable biglobal modes for the fully three-dimensional flow field will be discussed.