Let {X ; j ≥ 1} j be a sequence of weakly negative dependent (denoted by, WND) random variables with common distribution function F and let { ; j ≥ 1} j θ be other sequence of positive random variables independent of {X ; j ≥ 1} j and P[a ≤ ≤ b] = 1 j θ for some 0 < a ≤ b < ∞ and for all j ≥ 1. In this paper, we study the asymptotic behavior of the tail probabilities of the maximum, weighted sums, randomly weighted sums and randomly indexed weighted sums of heavy-tailed weakly negative dependent random variables, say, Σ Σ ≤ ≤ = = n j j j n j j n j j j X c X X 1 1 1 , , , max θ and Σ= N j j j X 1 θ , respectively , where {c j n} j ;1 ≤ ≤ are n bounded positive real numbers and N is a nonnegative integer-valued random variables, independent of i θ and i X for all i ≥1. In fact, for a large class of heavy-tailed distribution functions, we show that the asymptotic relations, [max ]~ [ ] ~ [ ], 1 1 1 Σ Σ ≤ ≤ = = > > > n j j j n j j n j j j j P θ X x P θ X x P θ X x hold as x → ∞. Finally, if E(N) < ∞ and also { ; j ≥ 1} j θ is a sequence of identical independent positive random variables, then we prove that [ ] ~ ( ). [ ], . 1 1 1 ∞ → > > Σ= P X x E N P X x as

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