We have studied the superconducting Tc(H) phase boundary of an A] superconducting disk with a perpendicularly magnetized dot on top of it. We used cylindrical and triangular dots. The inhornogeneous stray fields generated by these dots strongly affect the Tc(H) line, which now has the highest Tc at a finite applied field. This 'magnetic bias' of the T,(H) phase boundary depends on the magnetization of the dots. The field inhomogeneity leads to a pronounced modification of the T-C(H) periodicity. The theoretical Tc(H) dependence, calculated in the framework of the Ginzburg-Landau theory, fits Our experimental data very well. In a superconducting Pb film with a lattice of Co/Pd magnetic dots, field-induced superconductivity has been investigated. This remarkable effect appears due to the compensation of the returning stray fields of the dots by the applied magnetic field. As a result of the field compensation, the total field under the dots is enhanced, whereas in the areas between the dots the total field is strongly reduced, thus causing the field-induced superconductivity to appear. (c) 2005 Academie des sciences. Published by Elsevier SAS. All rights reserved.