"2003 Colloquium on Differential Equations and Applications, Maracaibo, Venezuela. Electronic Journal of Differential Equations, Conference 13, 2005, pp. 57-63. Title: On the solution of differential equations with delayed and advanced arguments Authors: Valentina Iakovleva (Univ.Simon Bolivar, Miranda, Venezuela) Carmen J. Vanegas (Univ.Simon Bolivar, Miranda, Venezuela) Abstract: In this work, we construct solutions to differential difference equations with delayed and advanced arguments. We use a step derivative so that a special condition on the initial function assures the existence and uniqueness of the solution. Published May 30, 2005. Math Subject Classifications: 34K15, 34K18. Key Words: Differential difference equations; functional differential equations.