We have investigated the dispersive properties of tunnelling-induced transparency in asymmetric double quantumwell structures where two excited states are coupled by resonant tunnelling through a thin barrier in a three-levelsystem of electronic subbands. The intersubband transitions exhibit high dispersion at zero absorption, which leads tothe slow light velocity in this medium as compared with that in vacuum (c＝3× 108). The group velocity in a specificGaAs/AlGaAs sample is calculated to be vg＝c/4.30. This structure can be used to compensate for the dispersion andenergy loss in fibre optical communications.