A random vector X=(X1, X2,…,Xm) is said to be negatively superadditive dependent (NSD) if for every superadditive function Φ, EΦ(X1, X2,…,Xm) ≤EΦ(Y1, Y2,…,Ym), where Y1, Y2,…, Ym are independent with Yi d= Xi for each i. Some basic properties and three structural theorems of NSD are derived and applied to show that a number of well-known multivariate distributions possess the NSD property. Applications are also presented.