In a quasi-two-dimensional (2D) electron system under a perpendicular magne
tic field, we have observed resonant interaction between intersubband Berns
tein modes and coupled intersubband-plasmon-LO-phonon modes. By changing pa
rameters of the 2D electron system, a transition from strong to weak regime
s of coupling between the plasmon and LO phonon was considered. In the stro
ng-coupling regime, we have observed a double-resonance splitting of the fi
rst intersubband Bernstein mode with both intersubband-plasmon-LO-phonon mo
des, whereas in the weak-coupling regime only a single resonance splitting
with the intersubband-plasmon-like mode has been found.