AbstractIn this paper we obtain an existence theorem for an integro-differential equation of the type u(s)+∫ω K(s,t) ∑α|⩽m (−1)|α| DαBα(t,ξ(u)(t)) dt=0. Hence ξ(u)(t) = {Dαu(t) : ¦ α ¦ ⩽ m} and Bα is a function of Ω × RSm in to R1.We assume that Bα satisfies “Nemytskii type” growth condition and also a monotonicity type condition. The kernel K is assumed to be such that it is in Wm,p(Ω × Ω) and is angle bounded. Our existence theorem is obtained by using the theory of monotone operators for Hammerstein operator equations.