We will present a notion of higher open book structure and its relationship with the existence of the real Milnor fibrations for non-isolated singularities polynomial map-germs. If time permits, we will see a topological invariant for the isolated singularity case. The first part of the talk was a joint work with Ying Chen and M. Tibar. The second part was with N. Dutertre and D. Dreibelbis.