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We consider particle motion in nonautonomous 1 degree of freedom Hamiltonian systems for which <em>H(p,q,t) </em>depends on <em>N</em> periodic functions of <em>t </em>with incommensurable frequencies. It is shown that in near-integrable systems of this type, phase space is partitioned into nonintersecting regular and chaotic regions. In this respect there is no different between the <em>N</em> = 1 (periodic time dependence) and the <em>N</em> = 2, 3, ... (quasi-periodic time dependence) problems. An important consequence of this phase space structure is that the mechanism that leads to fractal properties of chaotic trajectories in systems with <em>N</em> = 1 also applies to the larger class of problems treated here. Implications of the results presented to studies of ray dynamics in two-dimensional incompressible fluid flows are discussed.