Electronic Journal of Differential Equations, Vol. 2008(2008), No. 128, pp. 1-11. Title: A note on the existence of Psi-bounded solutions for a system of differential equations on R Author: Aurel Diamandescu (Univ. of Craiova, Romania) Abstract: We prove a necessary and sufficient condition for the existence of Psi-bounded solutions of a linear nonhomogeneous system of ordinary differential equations on R. Submitted April 10, 2008. Published September 18, 2008. Math Subject Classifications: 34D05, 34C11 Key Words: Psi-bounded solution; Psi-boundedenss; boundedness.