A theorem is presented that contains some sufficient conditions to ensure bound of solutions to a third-order nonlinear delay differential equation. It is shown that this theorem improves the result of Ponzo [On the stability of certain nonlinear differential equations, IEEE Trans. Automatic Control AC-10 (1965) 470-472] to the bound of solutions for the equation considered. (C) 2009 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.