THE NA (negatively associated) random variables are of considerable uses in system reliability and multivariate statistical analysis. Many authors have studied the limit properties for them. Definition 1. Random variables X,…,X(n≥2) are called NA if for every two distinct nonempty subsets Tand Tof {1,…,n} and every pair of coordinatewise nondecreasing (or nonincreasing) functions fand f, there holds