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Motivated by observations of surface drifters in the Adriatic Sea, transport in a three-gyre system is studied with the aid of dynamical systems techniques. Particular attention is paid to the issue of intergyre transport. The velocity field is assumed to be two-dimensional and incompressible and composed of a steady three-gyre background flow on which a time-dependent perturbation is superimposed. Two systems of this type are considered: 1) an observationally motivated, analytically prescribed model consisting of a steady background on which a multiperiodic time-dependent perturbation is superimposed, and 2) an observationally based model of the Adriatic Sea consisting of the mean surface circulation derived from surface drifter trajectories on which a time-dependent altimetry-based perturbation velocity field is superimposed. It is shown that for a small perturbation to the steady three-gyre background, two of the gyres exchange no fluid with the third gyre. When the perturbation strength exceeds a certain threshold, transport between all three gyres occurs. This behavior is described theoretically, illustrated using the analytic model and shown to be consistent with the observationally based model of the Adriatic. The relevance of the work presented to more complicated multiple-gyre problems is discussed. [ABSTRACT FROM AUTHOR]