A mechanism to explain the observed trapping or release of Lagrangian drifters by eddies is proposed, based on an interaction between the eddy circulation and the background flow. Eddies strong in relation to the background have a large “trap zone” within which particles are constrained to circulate in closed paths about the center, while relatively weak eddies have a smaller trap zone. Particles outside the trap zone drift freely, while those inside rotate with the eddy. As an eddy is advected by non‐uniform shear flow, its ‘trap zone’ expands or contracts so particles previously free become trapped or trapped particles are freed. Numerical experiments with idealized eddies embedded in different flows illustrate the concept. It is shown that drifters may begin to loop, as in some previously reported observations, without any need for eddy generation. Similarly, they may cease looping, without eddy destruction. The particular case of a strong cyclonic eddy south of Gran Canaria is modeled, using the observed density field and two drifter trajectories. Predicted drifter trajectories are compared with the observations. It is shown that the trajectories of buoys launched near the edge of the eddy are sensitive to small variations in the background field.