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We introduce two generalizations of Newton non‐degenerate singularities of hypersurfaces. Roughly speaking, an isolated hypersurface singularity is called  topologically Newton non‐degenerate  if the local embedded topological singularity type can be restored from a  collection  of Newton diagrams (for some coordinate choices). A singularity that is not topologically Newton non‐degenerate is called essentially Newton degenerate. For plane curves we give an explicit characterization of topologically Newton non‐degenerate singularities; for hypersurfaces we provide several examples.  Next, we treat the question of whether Newton non‐degenerate or topologically Newton non‐degenerate is a property of singularity types or of particular representatives: namely, is the non‐degeneracy preserved in an equisingular family? This result is proved for curves. For hypersurfaces we give an example of a Newton non‐degenerate hypersurface whose equisingular deformation consists of essentially Newton degenerate hypersurfaces.  Finally, we define the  directionally Newton non‐degenerate germs , a subclass of topologically Newton non‐degenerate ones. For such singularities the classical formulas for the Milnor number and the zeta function of the Newton non‐degenerate hypersurface are generalized.

On some generalizations of Newton non‐degeneracy for hypersurface singularities