In this paper, we study the existence of solutions of periodic boundary value problem for second-order nonlinear dynamic equations on time scales. For this purpose, we use two methods here. First, sign properties of the Green's function are investigated and existence results of bounded solutions of nonlinear boundary value problems are established as a result of Schauder fixed-point theorem. Second, the monotone method is discussed to assure the existence and uniqueness of solutions of such periodic boundary value problems on time scales. (C) 2004 Elsevier Ltd. All rights reserved.