One of the main reasons for studying Hammerstein operators is their possible application to the analytic study of nonlinear differential equations. In fact, the kernel ϕ used to represent such operators has properties similar to ones that insure the existence of solutions to equations of the form\(\dot x\)(t)=ϕ(x(t), t) or\(\dot x\)(t)= ϕ(x(t)). The main purpose of the present paper is to study limits of sequences of Hammerstein functionals. While these functionals fail to be linear, their adjoints (in the sense of J. Batt, see [3] and [4]) are linear operators. The Vitali-Hahn-Saks theorem is one of the main tools used to show that if the double adjoint of Tn converges on simple functions, then Tn converges to T uniformly over an appropriate set of continuous functions. Moreover, T is Hammerstein. Other results use the kernel representation of Tn and T. This situation is of particular interest when the double adjoints of Tn are dominated by probability measures.