Abstract: By using the characterization of heavy-tailed random variables in
$\mathcal{D}\cap\mathcal{L}$, precise large
deviations for sums (nonrandom sums and random sums) of negatively associated
heavy-tailed random variables in $\mathcal{D}\cap\mathcal{L}$ were obtained, where the
subclass $\mathcal{D}\cap\mathcal{L}$ strictly contains $\mathcal{C}$. Therefore, it
firstly extends some existed precise large deviation results to some larger subclasses
of heavy tailed distributions.

Key words: consistently varying tail, dominately varying tail, long tail, precise large deviation, negatively association, consistently varying tail, dominately varying tail, long tail, precise large deviation