Abstract: The basic properties of the nonlinear Landau-Zener tunnelling, a new quantum tunnelling phenomenon is reviewed, which is discovered in interacting two-level systems, such as Bose-Einstein condensates in optical lattices and molecule magnets. It is found that the nonlinearity induced by the repulsive interaction can enhance the tunnelling probability compared to the usual linear Landdau-Zener tunnelling. When the nonlinearity is strong enough, the adiabaticity can break down：an infinitely small external linear force can cause finite tunnelling probability.

Key words: Landau-Zener tunnelling, two-level system, adiabatic evolution