Rates of vibrational energy transfer in the five largest alpha helices and two largest coil segments of myoglobin are calculated and compared with energy transfer in one-dimensional glasses. In all three cases, vibrational energy transfer occurs by anharmonic coupling of spatially overlapping localized normal modes in resonance. The frequencies of pairs of localized vibrational modes close in space are usually separated by a few hundred cm(-1). As a result, there is little direct energy transfer to low-frequency modes by low-order anharmonic coupling, and rates of vibrational energy transfer from most higher-frequency modes are nearly temperature-independent, consistent with experimental observations. Variation of the anharmonic decay rate with mode frequency in helices and coils is similar, the trends of which are captured by an appropriately parametrized one-dimensional glass.