abstract: We consider the problem of prescribing the Q-curvature on the standard sphere S4 through a conformal change of metric. The problem is not always solvable because of some Kazdan-Warner obtructions, and some "topological" conditions on the function to be prescribed have to be imposed. We study the problem though a parabolic flow and reduce it to a finite-dimensional one via asymptotic analysis. Stationary points are then found using Morse theory. This is joint work with M.Struwe.