Let S(s,t) be a bivariate survival function. Let (S) over cap(n)(s,t) be the bivariate product limit estimator of S(s, t) proposed by Campbell and Foldes (1982, In: Gnedenko, B.V., Purl, M.C., Vincze, I. (Eds.), Nonparametric Statistical Inference. North-Holland, Amsterdam, pp. 103-122). In this paper, absolute moment and probability inequalities for S,,(s,t) are derived, respectively. (C) 2000 Elsevier Science B.V. All rights reserved.