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In this paper we study some properties of the class of ν-quasi-ordinary hypersurface singularities. They are defined by a very mild condition on its (projected) Newton polygon. We associate with them a Newton tree and characterize quasi-ordinary hypersurface singularities among ν-quasi-ordinary hypersurface singularities in terms of their Newton tree. A formula to compute the discriminant of a quasi-ordinary Weierstrass polynomial in terms of the decorations of its Newton tree is given. Thisdoi:10.17323/1609-4514-2013-13-3-365-398 fatcat:yvuz4yqs7vbx3hirqee7pyj2ty