Equations determining the velocity and density distributions within the mixing region of two incompressible gases with different densities are set up, their temperatures being assumed to be the same. For incompressible mixing the total number of gas molecules per unit volume is constant, although the density of the gaseous mixture varies from point to point due to diffusion of matter. As an illustration we consider the plane jet and steady motion. The boundary layer method of approximation can still be applied. The boundary of the jet is shown to be the same as that for one fluid. The solution of the problem then depends upon the numerical value of the coefticient of viscosity of the mixture which is a function of the number of molecules of each constituent gas in the unit volume. The present method of investigation is applicable to the cylindrical and half jets and also to the case where the two gases are at different temperatures.