Abstract: The existence of T-periodic solutions for the second order differential-iterative equation +g(x(x))=p(t) is studied, where g and p are continuous, p(t+T)=p(t),∫ T 0p(t)dt=0. A priori bounds are established for periodic solutions of the equation. By means of these bounds, an existence theorem for periodic solutions can be obtained by means of Mawhin’s continuation theorem. The results are proved under better conditions of g.