In this paper we continue with the study in any characteristic of equisingularity in codimension 1 started in [G-M]. The whclly general concept of equivalent singularities for plane curves introduced in [G-M] and [G-S], allows us to set out equisingularity in codimenson 1 in the case of positive characteristic, even in the non- equicharac-teristic and non-reduced cases. In this situation, we show the natural algebraic properties of equisingularity in codimension 1: good beharvior by monoidal dilatations, equisingularity of all special sections, characterization of the singular locus, etc. We also prove an equisingularity criterion which coincides with Lemma of [A2].