Chi-square processes for gene mapping in a population with family structure. The objective of this article to contribute to the genetic sequences of different individuals studies to identify chromosomal regions where the genetic variants are shared. The likelihood ratio test process related to the test of the absence of a quantitative trait locus (so called QTL) is considered on the interval representing a chromosome. New fast methods to compute critical values for QTL detection are proposed. The main result is formulated in two theorems is that the distribution of the LRT statistic is asymptotically that of the maximum of the square of I independent and “non linear interpolated Gaussian processes”. Methods are implemented in available Matlab package.