An exact solution for the zero boundary condition of the problem of carriers in spatially confined gapless semiconductors in a magnetic field is presented. Three cases are analysed: (i) the semiconductor occupies a half-space and the magnetic field orientatin is H ⟂ n (n is the surface normal); (ii) and (iii) a film of a gapless semiconductor at two orientations of the magnetic field, i.e. H ⟂ n and H | n respectively. It is shown that since the energy spectrum of gapless semiconductors is formed by strong relativistic spin–orbit interaction, significant peculiarities of the quantisation of the electron energy spectrum occur in all cases considered. Experiments to check the results obtained are discussed.