In　this　paper,　the　infinite　Prandtl　number　limit　of　Rayleigh-Benard　convection　is　studied.　For　well　prepared　initial　data,　the　convergence　of　solutions　in　L-infinity　(0,　t;　H-2(G))　is　rigorously　justified　by　analysis　of　asymptotic　expansions.