ABSTRACT The major purpose of this project is to apply Elzaki transform method supplemented with Adomain decomposition to solve nonlinear ordinary integro-differential equations. The basic concept of Elzaki transform, Adomain decomposition and integro-differential equation has been demonstrated. Applications of Elzaki transform method for solving nonlinear integrodifferential equations such as nonlinear Volterra integro-differential equations, nonlinear Fredholm integro-differential equations and the corresponding systems has been analyzed in this project. Keywords: Elzaki Transform, Adomain decomposition, nonlinear ordinary integro-differential equations.