Ordinary differential equations of fractional order have been presented as a tool of vital importance in modeling the anomalous dynamics of various problems from the exact sciences and engineering, however, is still under discussion a clear and coherent theory analogous to the classical theory of ordinary differential equations. The nonlocal character of their fractional operators provides additional information that allows the development of a comprehensive analysis of the mathematical models. Within these fractional order differential equations, the qualitative approach is an open topic of study at present, in which stability analysis plays a preponderant role. This article presents a description of recent results on the stability of nonlinear fractional order ordinary differential equations and some analytical methods used. First of all, this article presents and describes the fundamental concepts of the study of stability of systems of ordinary differential equations of fractional order, both linear and nonlinear. The results of this research provide fundamental tools in the study of the stability of systems of nonlinear fractional order differential equations that can be applied to various models of applied sciences and engineering. Keywords: fractional analysis, fractional differential equations, stability of fractional equations, Mittag-Leffler stability, Lyapunov functions. https://doi.org/10.55463/issn.1674-2974.50.7.7