Tungsten-carbene complexes of the type W(= CRR')(OR '')(2)X(2) . GaX(3) [CRR' = C(CH2)(3)CH2,C(CH2)(4)CH2, CHt-Bu or CHn-Bu; OR '' = OCH(2)t-Bu, OCD(2)t-Bu or Oi-Pr; X = Br or Cl] (I) have been used as catalysts to initiate ring-opening metathesis polymerization (ROMP) of cyclopentene, cycloheptene and cyclooctene (M). These reactions were followed by H-1 and C-13 NMR spectroscopy at variable temperature. Living polyalkenamers of the type W( = CHP)(OR '')(2)X(2) . GaX(3) [CHP = CHCmH2mCH = (CHCmH2mCH)(n-1) = CRR', m = 3 (cyclopentene), 5 (cycloheptene), 6 (cyclooctene); n greater than or equal to 1] (PC) were obtained in a first stage. These products undergo secondary metathesis reactions. In particular, intramolecular metathesis between the carbon-carbon double bonds and the tungsten-carbene chain-end function, within a given polymer chain, leads to regeneration of monomer or to cyclic oligomers. The thermodynamic equilibrium between these species is reached at varying rates depending on catalyst, monomer and temperature. For cyclopentene, only monomer was found at room temperature, while polypentenamers are the major species at low temperature. For cycloheptene, the corresponding polymerization equilibrium also exists, but is displaced more towards polyalkenamers. Moreover, the cyclic dimer, cyclotetradeca-1,8-diene (D), was obtained in high proportions under appropriate conditions, and its most stable trans, trans isomer was isolated from the reaction mixtures. For cyclooctene, conversion into polyoctenamers is rapid and complete at room temperature. In a third stage, catalysts I slowly convert olefins M, D and P into saturated polymers at room temperature. This reaction is also induced by GaBr3 alone. Complexes of the type W( = CRR') (OR '')(2)X(2) react similarly to their GaBr3 adducts, although much more slowly.