The amide vibrational modes play an important role in energy transport and relaxation in polypeptides and proteins and provide us with spectral markers for structure and structural dynamics of these macromolecules. Here, we present a detailed model to describe the dynamic properties of the amide I and amide II modes and the resulting linear and nonlinear spectra. These two modes have large oscillator strengths, and their mutual coupling plays an important role in their relaxation. Using first-principles calculations of NMA-d(7) and a dipeptide in a fluctuating bath described by molecular dynamics simulations, we model the frequencies of the local vibrations as well as the coupling between them. Both the coherent couplings and the fluctuations induced by contact with their environment are taken into account. We apply the resulting model of interacting fluctuating oscillators to study the collective vibrations and the partially coherent transport of vibrational energy through a model α-helix. We find that the instantaneous vibrations are delocalized over a few (up to four) amide units, while the coherences in the helix survive for 0.5-1 ps, leading to coherent transport on a similar time scale.