The nonparametric estimation of the survival function is discussed under thecompeting risks case where T_1,T_2,…,T_r may not be independent random varia-bles.Assume that(A·1)integral from 0 to t P(T_1>t/T=y,ξ(T)∈\bar{\varphi}_I)DS(y,\bar{\varphi}_I)=integral from 0 to t (S_I(t))/(S_I(y)) DS(y,\bar{\varphi}_I).Theorem 2.1.Let α=sup{t/S(t)>0}.Then the unique solution of S_I(t)=S(t,\varphi_I)+S(t,\bar{\varphi}_I)-integral from 0 to t (S_I(t))/(S_I(y)) DS(y,\varphi_I) has the follwing explicit expression:S_I(t) is a generalized self-consistent estimator if and only if there exist consistentestimators \hat{S}(t,\varphi_I) and \hat{S}(t,\bar{\varphi}_I),respectively,of S(t,\varphi_I) and S(t,\bar{\varphi}_I) such that (2.5)holds.Theorem 3.1.Under the condition of (A.1) and \hat{S}_I∈\phi_I,(ii) n~(1/2)((?)(t)-S_I(t)) converges weakly to a Gaussian p(?)ocess Z(t) for t in[0,T~*] with E(Z)=0 andcov(Z(s),Z(t))=S_I(s)S_I,(t) integral from 0 to s S~(-2)(y)DS(y,(?)),s≤T~*<α.If (?)(t) is a Bayesian estimator of S_I(t),then (?)(t) has similar properties.