Narasimhan and Ramanan used the $(0,1)$-stable bundles to define the Hecke curves on the moduli spaces of stable bundles over an algebraic curve. The Hecke curves have been used to study the geometry of the moduli spaces with fixed determinant. In particular, to describe minimal rational curves on the moduli space. Also to describe singular spectral curves and to study the moduli spaces of stable maps of rational curves. In this talk I will present some of the results of my student, Osbaldo Mata, on the generalization of the Hecke curves.