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Studying the appearance of active regions during periods of solar activity minima, we observed that the magnetic fields of active regions belonging to the old and new cycle were mutually related. This was the reason we decided to investigate the relation of the old and new cycle activity during the two last minima in more detail. We examined the distribution of both activities in heliographic longitude, because the patterns of such distribution change substantially during the time of the minimum, and we studied their relation to the distribution and development of the global (background) magnetic field. We observed that the active regions of the old and new cycles tended to concentrate in the same active longitudes. The sources of their magnetic fluxes seem to have the same heliographic longitude. The beginning of the new cycle activity, occurring at the very beginning to a very weak degree in the equatorial zone, and then proceeding to higher latitudes, occurs in the magnetic field remnants of the old cycle activity. During the transition phase, a relatively large number of small active regions is produced by both cycles.