The pinning of flux Lines by two different types of regular arrays of submicron magnetic dots is studied in superconducting Pb films; rectangular Co dots with in-plane magnetization are used as pinning centers to investigate the influence of the magnetic stray field of the dots on the pinning phenomena, whereas multilayered Co/Pt dots with out-of-plane magnetization are used to study the magnetic interaction between the flux lines and the magnetic moment of the dots. For both types of pinning arrays, matching anomalies are observed in the magnetization curves versus perpendicular applied field at integer and rational multiples of the first matching field, which correspond to stable Flux configurations in the artificially created pinning potential. By varying the magnetic domain structure of the Co dots with in-plane magnetization, a clear influence of the stray field of the dots on the pinning efficiency is found. For thr Co/Pt dots with out-of-plane magnetization, a pronounced field asymmetry is observed in the magnetization curves when the dots are magnetized in a perpendicular field prior to the measurement. This asymmetry can be attributed to the interaction of the out-of-plane magnetic moment of the Co/Pt dots with the local field of the flux lines and indicates that flux pinning is stronger when the magnetic moment of the dot and the field of the flux line have the same polarity. (C) 2000 Elsevier Science B.V. All rights reserved.