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SUMMARYA three-dimensional explicit time marching algorithm has been developed for the numerical solution of inviscid internal ows. The formulation uses the natural streamline co-ordinate system. The unsteady Euler equations in non-conservative form are expressed in terms of the extended Riemann variables and the ow angles. Along the characteristic trajectories in the space-time domain, these equations reduce to a system of ordinary di erential equations. Boundary conditions are also implemented in characteristic form. Shock waves are calculated after performing a one-point shock correction that maintains conservation across the discontinuity.The algorithm has been applied to subsonic, transonic and supersonic test cases. Despite the wide range in the Mach number and the diversity of the tested ow geometries, close agreement have been obtained with available analytical and numerical results.