The advanced tokamak scenario is of primary interest when considering the development of a steady state operating fusion facility. It is characterized by an improved core confinement and a large fraction of non-inductive toroidal plasma current. This non-inductive current is provided by the bootstrap current complemented by external sources. The current density profile of such scenarii often have an off-axis maximum, associated with a Negative Central magnetic Shear (NCS). The main operational limitations are due to MHD instabilities, leading to performance degradation or disruption. In this study we will focus on the Magneto-Hydro-Dynamic (MHD) stability of the plasma core of pulses which contain a hollow current profile (a very low current density near the magnetic axis), and with a large region of almost zero magnetic shear. A previous study showed that the resistive interchange mode was responsible for the filling of the hollow current profile in DIII-D. Later, it has been shown that the resistive kink prevented the current density from becoming negative, thus limiting the depth of the hollow current profile.