The estimation of the tail index in the context of heavy-tailed probability distributions has been extensively studied, particularly for independent and identically distributed (i.i.d.) data. However, the assumption of independence is not always realistic for real-world data, which has led researchers to develop estimation methods under various dependence structures, such as m-dependence, strong mixing, and weak dependence in the sense of Doukhan and Louhichi. In this work, we present the properties of two estimators of the tail index when applied to dependent data, analyzing their consistency and asymptotic properties under these different dependence structures.