This paper investigates the exponential stability and h-stability problems of some classes of nonlinear systems. First, we analyze the global uniform exponential stability for a class of integro-differential equations on time scales. We also derive some sufficient conditions for stability using an integral inequality approach. Then, we give an analysis of the h-stability of some classes of linear systems under Lipschitz-type disturbances. To this end, some h-stability criteria are established. Finally, numerical examples are proposed to illustrate the stability concepts.