Let Z(m,n) represent the mth largest (reverse) order statistic in a random sample of size n from a distribution F. Further let \(m=m(n)\) be an intermediate sequence of (n) in the sense that m/n\(\to 0\) and \(m\to \infty\) as \(n\to \infty\). The author finds the asymptotic joint distribution of order statistics of the form Z([mt],n), where \(00\) and \(\beta (.)>0.\) The author indicates that the joint distribution of these order statistics may be used for making statistical inferences about the upper tail of F, but this question is not pursued any further.