Structural relaxation in the peptide model N-methylacetamide (NMA) is studied experimentally by ultrafast optical Kerr effect spectroscopy over the normal-liquid temperature range and compared to the relaxation measured in water at room temperature. It is seen that in both hydrogen-bonding liquids, beta relaxation is present, and in each case, it is found that this can be described by the Cole-Cole function. For NMA in this temperature range, the alpha and beta relaxations are each found to have an Arrhenius temperature dependence with indistinguishable activation energies. It is known that the variations on the Debye function, including the Cole-Cole function, are unphysical, and we introduce two general modifications: One allows for the initial rise of the function, determined by the librational frequencies, and the second allows the function to be terminated in the alpha relaxation.