Anewiterativefully coupledimplicitspace-marching method isproposedforsolving thetwo-dimensionalsteady Eulerequationsforcompressiblee owsatMach numbers ranging from subsonic to supersonic. Aspecial treatment of the streamwise pressure gradient component permits us to calculate both supersonic e ow regions, where the Euler equations are hyperbolic, and subsonic regions, where the equations reveal elliptic properties. To take into account the elliptic effects of subsonic and transonic e ows, space-marching sweeps are carried out iteratively. A new parabolic pressure correction procedure is developed to accelerate the convergence rate. This procedure can be applied for subsonic and transonic regimes and is consistent with the characteristic analysis of the Euler equations.Ateach marching station,a Newton iterativetechniqueisused tosolvethenonlinearsystem ofequations in a fully coupled manner. To resolve strong shocks and contact discontinuities as well as smooth e owe elds with high accuracy, implicit symmetric second-order total variation diminishing and upwind second-order Richardson schemes are employed to approximate the transverse and streamwise derivatives, respectively. The method is tested on theproblem ofthee owin a ductwith a circulararcbump fordifferentMach numberregimes. Numerical calculations show that the method is accurate, is robust, and can efe ciently be applied for calculating subsonic, transonic, and supersonic e ows without streamwise separation.