Abstract: Electron cyclotron resonance CR) measurements have been carried out in magnetic fields up to 32 T to study electron-phonon interaction in two heavily modulation-delta -doped GaAs/Al0.3Ga0.7As single-quantum-well samples. No measurable resonant magnetopolaron effects were observed in either sample in the region of the GaAs longitudinal optical (LO) phonons. However, when the CR frequency is above LO phonon frequency, omega (LO)=E-LO/(h) over bar, at high magnetic fields (B>27 T), electron CR exhibits a strong avoided-level-crossing splitting for both samples at frequencies close to (omega (LO)+ (E-2-E-1)1 (h) over bar, where E-2, and E-1 are the energies of the bottoms of the second and the first subbands, respectively. The energy separation between the two branches is large with the minimum separation of 40 cm(-1) occurring at around 30.5 T. A detailed theoretical analysis, which includes a self-consistent calculation of the band structure and the effects of electron-phonon interaction on the CR, shows that this type of splitting is due to a three-level resonance between the second Landau level of the first electron subband and the lowest Landau level of the second subband plus one GaAs LO phonon. The absence of occupation effects in the final states and weak screening or this three-level process yields large energy separation even in the presence of high electron densities. Excellent agreement between the theory and the experimental results is obtained.