Zwanzig and Bixon have introduced a hydrodynamic model for self-diffusion, in which a single tagged particle moves through a viscoelastic continuum. After a small error in their calculation is corrected, it is shown that the agreement between theory and molecular-dynamics calculations of the velocity autocorrelation function is improved. We apply a similar type of model to the vibrational relaxation (dephasing and population relaxation) of a diatomic molecule in a monatomic fluid. The quantitative agreement with expectations from experiment is poor, suggesting a breakdown of the approach at the high frequencies involved in vibrational motion; however, the qualitative predictions of the model may be useful in correlating experimental data on vibrational Raman line shapes. Futhermore, the results imply that vibrational relaxation experiments in liquids will provide nonhydrodynamic information on the poorly understood high-frequency viscoelastic properties of liquids.