In this paper, we develop a generalisation of Roe's Riemann solver to the case of a mixture of perfect gases whose equation of state contains vibrational terms. Moreover, we assume that all species are at thermal equilibrium and that the temperatures of translation and vibration are the same. Then, we develop a semi-implicit scheme for the resolution of 1D problems for flows which are out of the chemical equilibrium. The Riemann solver to be used is the extension of Roe's solver which has been defined at the beginning of this report. In the last section, some shock tube problems are studied, they show the capacity of this method to solve such problems.