The content of this chapter consists of two parts. First, the stability and asymptotic stability of linear fractional differential equations with constant coefficients in arbitrary finite-dimensional spaces are discussed based on the fundamental solution expressed by the matrix-valued Mittag–Leffler function. Next, linear non-autonomous fractional differential systems are investigated with the fractional Lyapunov exponent. Some fundamental properties of this exponent are described and an application to the stability analysis of such systems is presented.