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We have investigated the behaviour of the depairing current J_{dp} in ferromagnet/superconductor/ferromagnet (F/S/F) trilayers as function of the thickness d_s of the superconducting layers. Theoretically, J_{dp} depends on the superconducting order parameter or the pair density function, which is not homogeneous across the film due to the proximity effect. We use a proximity effect model with two parameters (proximity strength and interface transparency), which can also describe the dependence of the superconducting transition temperature T_c on d_s. We compare the computations with the experimentally determined zero-field critical current J_{c0} of small strips (typically 5~ \mu m wide) of Fe/Nb/Fe trilayers with varying thickness d_{Nb} of the Nb layer. Near T_c the temperature dependence J_{c0}(T) is in good agreement with the expected behaviour, which allows extrapolation to T = 0. Both the absolute values of J_{c0}(0) and the dependence on d_{Nb} agree with the expectations for the depairing current. We conclude that J_{dp} is correctly determined, notwithstanding the fact that the strip width is larger than both the superconducting penetration depth and the superconducting coherence length, and that J_{dp}(d_s) is correctly described by the model., Comment: 10 pages, 5 figures, submitted to PR B