We investigate the existence of non-Bragg band gaps in 1D aperiodic photonic structures, namely the Fibonacci and Thue-Morse lattices combining ordinary positive index materials and dispersive metamaterials. Both structures present new band gaps which, in contrast with the usual Bragg gaps, are not based on interference mechanisms. It is known that one of these non-Bragg gaps corresponds to zero (volume) averaged refractive index. In this paper we demonstrate the existence of two new non-Bragg gaps in aperiodic photonic crystals: the zero permeability, and the zero permittivity gaps. Some distinctive aspects of these polarization-selective gaps are outlined and the impact on the photonic spectra produced by the level of the generation of the aperiodic structure is analyzed. © The Authors. All rights reserved [DOI: 10.2971/jeos.2007.07002]