Stability and asymptotic behavior of linear multi-time systems J/j(n)u(t) = AiU(t) + fi(t) is considered, where Ai are generators of commuting Co-semigroups on a Banach space. the authors formulate and prove versions of the results on exponential stability to homogeneous linear systems with multi-time. For non-homogeneous systems, the authors introduce the compatibility condition and obtain the variation-of-constants formula. Using simulta neous solutions of Sylvester equations, the authors obtain results on asymptotic almost periodicity of solutions.