The objective of this study is to obtain a better understanding of the fundamental mechanisms governing the unsteady flow past airfoil leading edges. The approach taken is to study the leading edge in isolation and to use the semi-infinite parabola as a model for the leading-edges of conventional airfoils. Numerical solution methods were developed and implemented for the two-dimensional, unsteady, incompressible Navier-Stokes and boundary-layer equations for arbitrary motion of the parabola. Navier-Stokes solutions of the impulsively-started flow past a stationary parabola and of the flow past a pitching parabola compare well with the corresponding computational results for the NACA0012 airfoil. Navier-Stokes solutions for the pitching leading edge were obtained for chord Reynolds numbers up to half-a-million. The sequence of events leading to the unsteady breakaway of the boundary layer, in both the impulsive and pitchup cases, was qualitatively similar for the range of Reynolds numbers considered;We show using Navier-Stokes simulations that small perturbations in the flow field can lead to the formation of eddies in the boundary layer before flow reversal occurs in the base flow. The cases considered here are impulsive changes in the angle of attack, smooth but rapid variations in the angle of attack and introduction of small-amplitude inviscid vortices in the freestream. This type of eddy creation prior to base-flow reversal is a feature of the high-frequency Rayleigh instability. A study of the Reynolds-number scaling of the wavelength of these instabilities yielded a value reasonably close to that predicted by theory. A linear stability analysis of the boundary layer over the parabola was carried out to map the neutral curve for the Rayleigh instability. Preliminary indications are that the disturbances that lead to the eddies in the Navier-Stokes simulations are being initiated within the linearly unstable region bounded by the neutral curve. The linear stability analysis showed that the Rayleigh instability occurs a little after boundary layer velocity profiles become inflectional but much before flow reversal sets in.