Abstract: Let (X_i⁰,Y_i⁰), 1 ≤ i ≤ n be i. i. d nonnegative random vectors with continuous survival distribution function be the product-limit estimator of S(s,t)=P(X⁰ > s,Y⁰ > t). Let S_n(s,t) be the product-limit estimator of S(s,t) suggested by Campbell and Földes (1980). In this paper it is shown that under some conditions a sequence of Gaussian processes G_n(s,t) can be constructed such that
sup_0T^0S|n^(1)/2[S_n(s,t)-S(s,t)]-G_n(s,t)|=O(n^-(1)/2 log²n) a. s.,for S,T which together satisfy a certain condition.

Key words: Strong Embedding, Product-Limit Estimator, Survival Distribution