We have investigated the intermediate valence narrow-gap semiconductor SmB6 at low temperatures using both conventional spear-anvil type point contacts as well as mechanically controllable break junctions. The zero-bias conductance varied between less than 0.01 mikrosiemens and up to 1 mS. The position of the spectral anomalies, which are related to the different activation energies and band gaps of SmB6, did not depend on the the contact size. Two different regimes of charge transport could be distinguished: Contacts with large zero - bias conductance are in the diffusive Maxwell regime. They had spectra with only small non-linearities. Contacts with small zero - bias conductance are in the tunnelling regime. They had larger anomalies, but still indicating a finite 45 % residual quasiparticle density of states at the Fermi level at low temperatures of T = 0.1 K. The density of states derived from the tunelling spectra can be decomposed into two energy-dependent parts with Eg = 21 meV and Ed = 4.5 meV wide gaps, respectively.