Stereospecificity and enantioasymmetry of living polymerization of methylthiirane initiated by various bis(alkyl-S-cysteinato)cadmium are studied. Whatever the alkyl group structure R used, we always observe the same general feature for this living polymerization. Two types of chiral sites C-R(*) and C-S(*) are present leading to an isotactic polymer. The preferential incorporation of the R enantiomer implies that active sites may be present in different amounts and/or with different reactivities. Isomeric relationship between the two types of active sites is depending on the <(Mn)over bar> of the growing chain bearing them and two separate stages are observed. In the first step, when the two types of active sites are diastereoisomers (for <(Mn)over bar> of the growing chain bearing the active sites contained between 6000 and 35000) we observe an effect of R on the enantioasymmetry. Stiff alkyl groups lead to relatively high enantioasymmetric constants whereas for long chains (2-octyl), the enantioasymmetry practically disappears.In the second step, when the molar weight of the growing chain bearing the active sites is higher than 35000, the enantioasymmetry polymerization run on the enantiomeric form of active sites does not depend on the alkyl group.