Semiconductor superlattices may display dispersions that are degenerate either at the zone center or zone boundary [G. Bastard, Wave Mechanics Applied to Semiconductor Heterostructures, Monographies de Physique (Les Editions de Physique, Les Ulis, 1988); C. Sirtori, F. Capasso, D. L. Sivco, and A. Y. Cho, Appl. Phys. Lett. 64, 2982 (1994)]. We show that they are linear upon the wave vector in the vicinity of the crossing point. This establishes a realisation of massless Dirac bands within semiconductor materials. We show that the eigenstates and the corresponding Wannier functions of these superlattices have peculiar symmetry properties. We discuss the stability of the properties of such superlattices versus the electron in-plane motion. As a distinct fingerprint, the inter-sub-band magnetoabsorption spectrum for such superlattices is discussed.