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In this paper, two discriminative training procedures for a Gaussian mixture model (GMM) language identification system are described. One is based on maximum mutual information criterion (MMI), the other uses minimum classification error (MCE) criterion. Both the proposals are based on the generalized probabilistic descent (GPD) algorithm formulated to estimate the GMM parameters. The evaluation is conducted using the OGI multi-language telephone speech corpus. The experimental results show such system is very effective in language identification tasks.