Two-vibron bound states in the CO monolayer adsorbed on Ru(001) are investigated by using an attractive Hubbard Hamiltonian for boson with long-range lateral interactions. The parameters which characterize this Hamiltonian are determined through an accurate comparison between the present theory and previous experimental results. In a perfect agreement with experimental data, an anharmonic shift equal to 31.12 cm(-1) is obtained. It is pointed out that the anharmonicity depends on the CO coverage which originates in a chemical modification of the intramolecular CO potential due to surrounding molecules. The anharmonicity is responsible for the occurrence of a two-vibron bound states band located at approximately 20 cm(-1) below the free states continuum. This band exhibits a rather weak dispersion, equal to 3.28 cm(-1), almost 30 times smaller than the two-vibron free states continuum bandwidth equal to 100 cm(-1). Although long-range lateral interactions favor a large free states continuum, it is shown that the range of the coupling does not modify significantly the bound states band. (C) 2003 American Institute of Physics.