Summary: Let \(\{X_{n}, n \geq 1\}\) be an \(R\)-valued stochastic process with a common probability density function \(f(x)\), distribution function \(F(x)\) and survival function \(\overline {F}(x) = 1 - F(x) = P(X > x)\). We suppose that the process is strongly mixing and the empirical survival function \(\overline {F_{n}}(x)\) based on \(X_{1}, \cdots , X_{n}\) is proposed as an estimator for \(F(x)\). Strong consistency and pointwise as well as uniform asymptotic normality of \(\overline {F_{n}}(x)\) are discussed.