In　this　article,　two　relaxation　time　limits,　namely,　the　momentum　relaxation　time　limit　and　the　energy　relaxation　time　limit　are　considered.　By　the　compactness　argument,　it　is　obtained　that　the　smooth　solutions　of　the　multidimensional　nonisentropic　Euler-Poisson　problem　converge　to　the　solutions　of　an　energy　transport　model　or　a　drift　diffusion　model,　respectively,　with　respect　to　different　time　scales.