Theoretical studies on ethene metathesis reaction proceeding on molybdenamethylidene centres of molybdena-alumina catalyst are reported. Calculations were carried out with the Gaussian 94 program, using density functional theory. Models of active sites containing Mo-VI and Mo-IV (both singlet and triplet state) have been developed. Molybdenum in these centres is attached to a cluster of formula Al-2(OH)(6), which represents alumina. The thermodynamics of the reactions of ethene with Mo-VI and Mo-IV carbene centres were calculated. The reaction pathways of ethene addition to Mo-VI and Mo-IV methylidene complexes were also investigated. In these calculations simpler structures of the carbene and molybdacyclobutane complexes have been applied, in which the bonds between molybdenum and the carrier are replaced by hydroxyl groups. It was concluded that active centres of ethene metathesis do not contain Mo-IV because of high energy barriers of some elementary steps of the process.