This paper describes the use of several kinds of group TV Cp based catalyst systems, in the synthesis of co- and terpolymers of ethylene, propylene and alpha-olefins endowed with OH and COOH functional groups. The hydroxy monomers used were 5-hexen-l-ol (4) and 10-undecen-1-ol (5) and the carboxy monomer was 10-undecen-1-oic acid (6). The three catalyst systems used were the C-2 symmetric ansa-zirconocene (1) the "in-site" titanium complex (2) and the non-rigid zirconocene (3), all activated by methylaluminoxane. Trimethylaluminium was used to protect the functional group of polar monomers. The first two catalyst systems suffer similar activity loss in the presence of polar monomer whereas the third one exhibited better tolerance toward the hydroxyolefins. NMR and FTIR spectroscopies were used to characterize the polymerization products. All three catalyst systems afforded functionalized co- and terpolymers by direct polymerization of ethylene/propylene/hydroxy-alpha-olefins but only the catalyst system ((1)/MAO displays appreciable activities for direct polymerization of ethylene, propylene and carboxy-co-olefins.