2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/122211A criterion for the HNN-extension of a finite p-group to be residually a finite p-group is obtained and based on this criterion the sufficient condition for residuality a finite p-group of HNN-extension with arbitrary base group is proved. Then these results are applied to give for groups from two classes of one-relator groups the necessary and sufficient condition to be residually a finite p-group.12 pages. This is a translation from Russian of the paper published in Vestnik of Ivanovo State University, 2000, issue 3, p. 129-140Group Theory20E26, 20E06text