2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58520We study an analogue of the classical Bianchi-Darboux transformation for L-isothermic surfaces in Laguerre geometry, the Bianchi-Darboux transformation. We show how to construct the Bianchi-Darboux transforms of an L-isothermic surface by solving an integrable linear differential system. We then establish a permutability theorem for iterated Bianchi-Darboux transforms.13 pages, amstex, to be published in IJMDifferential Geometry53A40, 53A05text