The tail behavior of Hodges-Lehmann type location estimators is studied with respect to a tail performance measure. The result obtained here generalizes and complements the corresponding work on R-estimators of JurecKova (1981a). The connection between the tail behavior and the breakdown point discovered in He, Jureckova Koenker and Portnoy (1990) for regression and monotone location estimators is extended to Hodges-Lehmann type location estimators, confirming the important role of the tail behavior as a measure of robustness of estimators.