The decay of excited stretching overtones of some local modes (C–H, C 3/4 C,C=C, C=O) attached to a hybrocarbon chain is theoretically investigated. The assumptions used in a previous paper [A. Lami and G. Villani, J. Chem. Phys. 88, 5186 (1988)] are critically examined and the model is improved by allowing the transfer of up to three quanta from the local mode (simulated by a Morse oscillator) to the harmonic bath of the chain modes. Use is made of a Lanczos tridiagonalization procedure. It is shown that the population transfer from the local mode to an aliphatic carbon chain is rapid but not complete due to the fact that the local mode frequency lies above the top of the band of chain modes and to the particular structure of the Hamiltonian for kinetically coupled stretching modes. It is argued that the complete decay should involve other low frequency modes and should require a longer time.