In this paper, a new free-text speaker verification method is proposed. This method uses a modeling of the spectral evolution of the speech signals, which is capable of processing some aspects of the inter-speaker variability : the AR-Vector models. To learn Discriminant AR-Vector models, three training techniques are proposed. These techniques are used to reduce the verification computation cost. The difficult choice of the impostor rejection criterion in the verification systems is discussed. The evaluation of this method is carried out on the TIMIT database recorded by cooperative speakers without impostor. A series of free-text speaker verification experiments are described. There is no specific corpus for the training sentences and the training corpus is different from the test corpus. The verification tests are made in the difficult conditions: for each experiment, a speaker is taken out of the database and is played impostor posing as the all database speakers. The experiments give first-rate results (i.e, verification rate of 99.8% for 630 speakers) without using more than two sentences for each test.