We investigated the behavior of waveguide resonance modes in a metamaterial consisting of metallic slit-array slabs separated by an air gap. Simulation results show two unusual types of intersection phenomena. One type is an anticrossing with a specifically recognizable mode repulsion. An effective medium theory analysis revealed that this phenomenon can be explained in terms of an increased effective refractive index in the air-gap region. The other type of intersection leads to transmission suppression by the mixing of symmetric and asymmetric modes. This fade-out phenomenon is associated with a change in the behavior of the symmetric mode above a critical frequency. (C) 2016 The Japan Society of Applied Physics