Ethene/1-olefin blocky copolymers were obtained through nonliving insertion copolymerizations promoted by an isospecific single site catalyst. Propene or 4-methyl-1-pentene were copolymerized with ethene with metallocenes endowed with different stereospecificity in propene polymerization: (i) aspecific "constrained geometry" half-sandwich complex, {eta(1):eta(5)-([tert-butylamido)dimethylsilyl](2,3,4,5-tetramethyl-1-cy clopentadienyl)}titanium dichloride [Me2Si(Me4Cp)(N-Bu-t)TiCl2] (CG), (ii) moderately isospecific rac-ethylenebis(indenyl)zirconium dichloride [rac-(EBI)ZrCl2] (EBI), (iii) slightly more isospecific hydrogenated homologue, rac-ethylenebis(tetrahydroindenyl) zirconium dichloride [rac-(EBTHI)ZrCl2] (EBTHI), (iv) highly iso-specific rac-[methylenebis(3-tert-butyl-1-indeny)]zirconium dichloride [rac-H2C-(3-(t)Bulnd)(2)ZrCl2] (TBI), (v) most isospecific rac-lisopropylidene-bis(3-tert-butyl-cyclopentadienAzirconium dichloride [rac-Me2C-(3-(BuCp)-Bu-t)(2)ZrCl2] (TBC). Copolymerizations were described by a 2(nd) order Markovian copolymerization model and data are proposed to correlate the formation of 1-olefin sequences with catalytic site isospecificity, made by the cooperation of organometallic complex and growing chain. Blocky copolymers were prepared over wide ranges of compositions: with any of the isospecific metallocenes when 4-methyl-1-pentene was the 1-olefin and only with the highly isospecific ones (TBI, TBC) when propene was the comonomer. A penultimate unit effect was observed with TBI as the metallocene, whereas a 1 order Markov model described the ethene/propene copolymerization from TBC. A moderately isospecific metallocene, such as EBI, is shown to be able to prepare blocky ethene copolymers with 4-methyl-1-pentene. These results pave the way for the synthesis of new ethene based materials. (C) 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 2063-2075,2010