2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/163976In the study of equisingularity of isolated singularities we have the classical theorem of Briancon, Speder and Teissier which states that a family of isolated hypersurface singularities is Whitney equisingular if and only if the mu^*-sequence for a hypersurface is constant in the family. In this paper we generalize to non-isolated hypersurface singularities. By assuming non-contractibility of strata of a Whitney stratification of the non-isolated singularities outside the origin we show that Whitney equisingularity of a family is equivalent to constancy of a certain selection of invariants from two distinct generalizations of the mu^*-sequence. Applications of this theorem to equisingularity of more general mappings are given.The new version clarifies part of Lemma 5.2 and contains a new proposition that justifies a step in Lemma 5.3 (now 5.4) that no-one seemed to believeAlgebraic GeometryComplex Variables32S15; 32S30; 32S60text