In this paper we extend the classification scheme in [S] for bm-symplectic surfaces, and more generally, bm-Nambu structures to the equivariant setting. When the compact group is the group of deck-transformations of an orientable covering, this yields the classification of these objects in non-orientable manifolds. The paper also includes recipes to construct bm-symplectic structures on surfaces. Feasibility of such constructions depends on orientability and on the colorability of an associated graph. We recast the strategy used in [MT] to classify stable Nambu structures of top degree on orientable manifolds to classify bm-Nambu structures (not necessarily oriented) using the language of bm-cohomology. The paper ends up with an equivariant classification theorem of bm-Nambu structures of top degree.