Summary: We show that the three-dimensional supersonic gas flow past an infinite cone is nonlinearly stable upon the perturbation of the obstacle. The perturbed flow exists globally in space and tends downstream to a self-similar flow. There is a thin layer of concentration of vorticity and entropy variation. Our analysis is based on an approximation, using local self-similar solutions as building blocks. This enables us to obtain global estimates for nonlinear wave interactions needed for the stability analysis.