We consider the likelihood ratio test (LRT) process related to the test of the absence of QTL on the interval [0, T] representing a chromosome (a QTL denotes a quantitative trait locus, i.e. a gene with quantitative effect on a trait). We give the asymptotic distribution of this LRT process under the null hypothesis that there is no QTL on [0, T] and under the alternative that there exists a QTL at t* on [0, T]. We show that the LRT is asymptotically the square of non linear interpolated process. We propose a simple and original method to calculate the maximum and the argmax of the LRT process using only statistics on markers and their ratio. We finally propose a new method to calculate thresholds for QTL detection.