Electronic Journal of Differential Equations, Vol. 2010(2010), No. 152, pp. 1-16. Title: Stability properties of differential systems under constantly acting perturbations Authors: Giancarlo Cantarelli (Univ. di Parma, Italy) Giuseppe Zappala (Univ. di Parma, Italy) Abstract: In this article, we find stability criteria for perturbed differential systems, in terms of two measures. Our main tool is a definition of total stability based on two classes of perturbations. Submitted January 17, 2010. Published October 21, 2010. Math Subject Classifications: 34D20, 34C25, 34A34. Key Words: Stability; persistent disturbance; two measures; Liapunov functions.