Molecular excited vibrational states are metastable states and we incorporate their finite lifetimes into the theory of vibrational energy transfer between weakly interacting molecules, i.e., at internuclear distances at which they do not have a chemical bond. Expressions for the effective lifetime of an initially vibrationally excited molecule in the presence of a neighboring molecule are derived in closed form. These expressions allow one to analyze the physics behind the energy transfer. It is shown that due to different finite lifetimes of the isolated excited molecules, a very efficient vibrational energy transfer can take place between them even if their energies are rather off-resonance. Examples are discussed.Vibrations constitute a fundamental property of molecules and of other matter made of molecules. Excited vibrational molecular levels in the electronic ground state decay rather slowly radiatively, their radiative lifetime is typically in the range of seconds to milliseconds [1], see also [2]. In contrast, fast non-radiative lifetimes in the range of pico-and even femtoseconds have been reported for even small polyatomic molecules [3][4][5]. The underlying mechanism of intramolecular vibrational energy redistribution (IVR) has attracted much attention for several decades [3][4][5][6][7][8]. Here, an optically active vibrational mode couples to other modes which in turn couple to other modes (tier model [5,9]) redistributing the energy of the initially excited mode over other parts of the molecule. Anharmonic coupling plays here a decisive role. We shall return to the IVR below.The presence of IVR suggests the investigation of the more general subject of vibrational energy flow in molecules which has become an active field of research (for a recent review see [10]). Multidimensional spectroscopy experiments and theoretical investigations provide valuable information on this flow and hence on vibrational energy transport (or transfer) in condensed phase molecular systems, see, e.g., [11][12][13][14][15] and references therein. The major driving force of vibrational energy transfer is again anharmonicity [14][15][16].In this work we investigate the possibility for vibrational energy transfer between weakly interacting molecules, i.e., between molecules at distances where chemical bonds are not formed. We show that indeed such a transfer can be efficient even if it is not resonant, i.e., the respective levels are rather far from matching. The main ingredient is that the participating vibrational excited levels are metastable states of finite lifetimes. These lifetimes can be due to radiative decay, IVR or any other kind of decay, like predissociation. Consider a molecule 1 with a vibrational state of complex energy E 1 − iΓ 1 /2 which interacts with a vibrational state of a neighboring molecule 2 of complex energy E 2 − iΓ 2 /2, where Γ is the width of a level of lifetime τ = /Γ [17,18]. The time-evolution of the coupled metastable states (also called resonances) is governed by the Schroedinger equa-wher...