Suppose that {X

i

}

i≥1

is a sequence of nonnegative and nonidentically distributed random variables which belong to the subclass of heavy-tailed distributionsclass C. The multivariate distribution function of the random variables is governed by the FGM copula function. The uniformly asymptotic estimate for the partial sums and random sums of the sequence {X

i

}

i≥1

are studied

respectively. The obtained results extend the corresponding asymptotic estimate of the tail probability of the dependent random variables.