Consider a two-dimensional renewal risk model, in which the claim sizes {(X)k;k≥1} form a sequence of independent, identically distributed (i.i.d.) and non-negative random vectors with a joint distribution function F12 ; by allowing the two components of the random vectors to be dependent.Suppose that the claim sizes and inter-arrival times form a sequence of i.i.d.random pairs, with each pair obeying a dependence structure via the conditional distribution of the inter-arrival time given the subsequent claim size being large, and then a precise large deviation of the aggregate amount of claims is obtained.