This paper presents a central limit theorem for a sequence of dependent random variables under the assumption of a strong mixing condition. The theorem is of interest because it formalizes a heuristic notion of A. Markoff, suggesting that a central limit theorem holds for dependent variables if they behave more like independent variables as they become more separated. The strong mixing condition is a more intuitive formalization of this notion than most others and is also a strong version of the mixing condition in ergodic theory. The mixing condition is defined for sets of the form $ a_{kr} < X_{kr} \leq b_{kr} $, where $ k_1 < \ldots < k_s $. The distance between two such sets is defined as the distance between the intervals containing their indices. The strong mixing condition is satisfied if $ |P(A \cap B) - P(A)P(B)| < f(d(A, B)) $, where $ f(n) $ is a function decreasing to zero as $ n \to \infty $. The central limit theorem is established under the assumption that the mean values $ EX_k \equiv 0 $ and certain conditions on the second and $ 2 + \delta $ order moments. The paper shows that $ S_n / \sqrt{kh(p_n)} $ is asymptotically normally distributed. This is achieved by showing that the sum of certain terms tends to zero in probability and by applying the Tchbycheff inequality and Lemma 2. The result includes the results of Höffding and Robbins. The paper also discusses the strength of the strong mixing condition compared to the ordinary mixing condition in the case of a strictly stationary process. The sequences $ k, p_n, q_n $ are chosen such that $ kp_n \sim n $, $ q_n / p_n \to 0 $, and $ kh(q_n) / h(p_n) \to 0 $, ensuring the asymptotic normality of $ S_n / \sqrt{kh(p_n)} $.This paper presents a central limit theorem for a sequence of dependent random variables under the assumption of a strong mixing condition. The theorem is of interest because it formalizes a heuristic notion of A. Markoff, suggesting that a central limit theorem holds for dependent variables if they behave more like independent variables as they become more separated. The strong mixing condition is a more intuitive formalization of this notion than most others and is also a strong version of the mixing condition in ergodic theory. The mixing condition is defined for sets of the form $ a_{kr} < X_{kr} \leq b_{kr} $, where $ k_1 < \ldots < k_s $. The distance between two such sets is defined as the distance between the intervals containing their indices. The strong mixing condition is satisfied if $ |P(A \cap B) - P(A)P(B)| < f(d(A, B)) $, where $ f(n) $ is a function decreasing to zero as $ n \to \infty $. The central limit theorem is established under the assumption that the mean values $ EX_k \equiv 0 $ and certain conditions on the second and $ 2 + \delta $ order moments. The paper shows that $ S_n / \sqrt{kh(p_n)} $ is asymptotically normally distributed. This is achieved by showing that the sum of certain terms tends to zero in probability and by applying the Tchbycheff inequality and Lemma 2. The result includes the results of Höffding and Robbins. The paper also discusses the strength of the strong mixing condition compared to the ordinary mixing condition in the case of a strictly stationary process. The sequences $ k, p_n, q_n $ are chosen such that $ kp_n \sim n $, $ q_n / p_n \to 0 $, and $ kh(q_n) / h(p_n) \to 0 $, ensuring the asymptotic normality of $ S_n / \sqrt{kh(p_n)} $.