  We analyze the transport properties in approximants of quasicrystals
alpha-AlMnSi, 1/1-AlCuFe and for the complex metallic phase lambda-AlMn. These
phases presents strong analogies in their local atomic structures and are
related to existing quasicrystalline phases. Experimentally they present
unusual transport properties with low conductivities and a mix of metallic-like
and insulating-like characteristics. We compute the band structure and the
quantum diffusion in the perfect structure without disorder and introduce
simple approximations that allow to treat the effect of disorder. Our results
demonstrate that the standard Bloch-Boltzmann theory is not applicable to these
intermetallic phases. Indeed their dispersion relation are flat indicating
small band velocities and corrections to quantum diffusion that are not taken
into account in the semi-classical Bloch-Boltzmann scheme become dominant. We
call this regime the small velocity regime. A simple Relaxation Time
Approximation to treat the effect of disorder allows us to reproduce the main
experimental facts on conductivity qualitatively and even quantitatively.
