A thorough analysis of Energetic Particle Modes (EPM) stability and mode structures is presented for tokamaks with hollow q-proles. Focusing on the region near the minimum-q surface, EPM gap modes and resonant EPMs are shown to exist as solutions of the same dispersion relation. By controlling the fast ion distribution function, or, equivalently, their fundamental dynamical properties, a smooth transition between these two classes of modes is obtained within the EPM dispersion relation. When toroidal coupling becomes important, it is demonstrated that EPMs may have either single or double hump radial structures. The local analyses of EPM stability and mode structures near the minimum-q surface are put in the broader framework of EPM stability and EPM induced transport in tokamaks with hollow q-proles and a brief summary is also given of present understanding of such problems based on results of 3D non-linear hybrid Magneto Hydro Dynamic-Gyrokinetic simulations. Possible implications of present results are discussed in terms of experimental observations and possibilities of designing novel experimental set-ups to probe, at least conceptually, the complex predictions of theory.