We use photometric data from the TESS space observatory and optical catalogs of stars in the Pleiades, Hyades, and Blanco 1 open clusters that contain 2226, 790, and 752 sources selected based on Gaia data. Using various statistical periodicity estimation methods, such as SNR and PDM, and taking into account the TESS angular resolution (1 pixel=21"), we have determined the periods for 635, 222, and 98 stars in the Pleiades, the Hyades, and Blanco 1, respectively. The search for periodic signals was limited to 13 days, since the light curve duration in one TESS sector is about 27 days, while the use of several successive sectors is made difficult by the zero-point offset of the instrumental flux between them. Supplementing our results by information from the VizieR database, we have found that the periods were estimated for 1290 (58%), 584 (74%), and 250 (33%) stars in the Pleiades, the Hyades, and Blanco 1, respectively. Among them, for 44, 28, and 12 sources in these clusters the periods have been determined for the first time. Thus, in this paper we present the most complete catalog of periods of stars in these clusters.