We present the first evidence for a distinct optical phonon progression in the linear and nonlinear intersubband absorption spectra of electrons in a GaN/Al(0.8)Ga(0.2)N heterostructure. Femtosecond two-color pump-probe experiments in the midinfrared reveal spectral holes on different vibronic transitions separated by the LO-phonon frequency. These features wash out with a decay time of 80 fs due to spectral diffusion. The remaining nonlinear transmission changes decay with a time constant of 380 fs. All results observed are described by the independent boson model.