Lyapunov stability and asymptotic stability conditions for the solutions of the fractional integrodiffrential equations x ( α ) ( t ) = f ( t , x ( t ) ) + ∫ t 0 t k ( t , s , x ( s ) ) d s , 0 < α ≤ 1 , with the initial condition x ( α − 1 ) ( t 0 ) = x 0 , have been investigated. Our methods are applications of Gronwall's lemma and Schwartz inequality.