The interdiffusion problem of two alloys is studied. It is assumed that the alloys are brought into contact and then heated to a fixed temperature. The problem is considered to be one-dimensional, the time dependent change of concentration being caused by convective and diffusive fluxes, with the diffusion coefficient depending on the local concentration. The paper contains the definition of a weak solution, the proof of a regular solution and a proposal for a numerical solution, which is split into a parabolic and a hyperbolic part. The hyperbolic problem is solved by using an upwind scheme, and the parabolic one by a linearized backward Euler method in time with a finite element space discretization. Finally, the authors report the convergence of the numerical scheme and mention, that the results obtained with the solution are in accordance with experimental data.