Abstract: Two forms of implicit TVD schemes are proposed in this paper for the simulation of nonequilibrium flows past hypersonic re-entry vehicle, which are derived from the diagonal form of an approximate-factorization algorithm and lower-upper scheme applied to the implicit part of Harten-Yee's TVD scheme respectively. Numerical tests are taken for the two-dimensional and three-dimensional chemically nonequilibrium flows, and the results demonstrate that the algorithms in the paper are both efficient with high-resolution and less cost in computation.