Let Xλ1,Xλ2, . . . , Xλn be independent non negative random variables with, Xλi~F(λi t ), i = 1, . . . , n, where λi > 0, i = 1, . . . , n and F is an absolutely continuous distribution. It is shown that, under some conditions, one largest order statistic Xλ

n: n is smaller than another one Xθ

n: n according to likelihood ratio ordering. Furthermore, we apply these results when F is a generalized gamma distribution which includes Weibull, gamma and exponential random variables as special cases.