TITLE: Existence and measure of 2-quasiperiodicity in Hamiltonian one-and-a-half degree of freedom systems AUTHORS: H.W. Broer^(1), M. van Noort^(2), C. Sim\'o^(3) (1) Department of Mathematics and Computer Science, University of Groningen, P.O. Box 800, 9700 AV Groningen, Netherlands (2) School of Mathematics Georgia Institute of Technology,Atlanta, GA 30332-0160 USA (3) Departament de Matem\`atica Aplicada i An\`alisi, Universitat de Barcelona, Gran Via, 585, 08071 Barcelona, Spain ABSTRACT: The goal of this paper is to show some properties of real analytic Hamiltonian systems of the form $H=\frac{1}{2}y^2+V(x,t), where $V$ is periodic in $x$ and $t$. We prove that this system has invariant tori of rotational type for sufficiently large values of $|y|$. The measure of the set of such tori is shown to be exponentially close to full measure as $y \to \pm \infty.$