The transition temperature and the critical fields of electron-beam evaporated Nb/Gd/Nb triple layers and Nb/Gd multilayers have been determined by measurements of the electrical resistivity and the dc susceptibility. For constant thickness d(Gd) of the Gd layers, we observe a decrease of T(c) and H(c2 perpendicular-to) with decreasing thickness d(Nb) of Nb layers down to a critical thickness d(c), below which superconductivity is completely destroyed. The parallel critical fields mostly show the square-root temperature dependence near T(c), typical for two-dimensional superconductors. As predicted theoretically, competing pair-breaking mechanisms lead to a nonmonotonic dependence of H(c parallel-to) on d(Nb). We have also studied the dependence T(c)(d(Gd)) with constant d(Nb) and find a decrease of the T(c)(d(Gd)) curve with increasing d(Cd) and a steplike structure at d(Gd) almost-equal-to 20 angstrom. To clarify the nature of this step, the ferromagnetic transition of the Gd films is determined with the transverse magneto-optical Kerr effect. Long-range magnetic order is found only above d(Gd) almost-equal-to 20 angstrom, which is attributed to the formation of a discontinuous film below this thickness. These results indicate a change in the underlying pair-breaking mechanism.