Rank-based estimators were proposed by Clayton (1978) and Oakes (1982) for the association parameter in the bivariate gamma frailty model. The joint asymptotic behavior of these estimators is considered here, following a different approach from that used by Oakes (1982, 1986). This leads to a correction of the formula given by Shih (1998) for the limiting covariance between the two estimators.