[(R,R)-Bco-dpp]PtCl2 (3; Bco-dpp is (R,R)-[bicyclo[2.2.2]octane-3,4-diylbis(methylene)]bis(diphenylphosphine)) and [(R,R)-Bco-dbp]PtCl2 (4; Bco-dbp is (R,R)-[bicyclo[2.2.2]octane-3,4-diylbis(methylene)]bis(5H-benzo[b]phosphindole)) have been synthesized and used as the catalyst precursors in the presence of SnCl2 for the enantioselective hydroformylation of some olefinic substrates. The catalytic activity of these systems is very high. The level of asymmetric induction caused by 3 remains rather low. However, the capacity for enantioface discrimination displayed by 4 is the highest reported for the hydroformylation of styrene to hydratropaldehyde (best optical yield approximately 86.3 %) and 1-butene (best optical yield approximately 67 %). In the case of styrene this high enantioselectivity is accompanied by an excellent regioselectivity (80 % of the branched isomer). The enantioselectivity shown by 4 was not improved by carrying out the reaction in the presence of triethyl orthoformate. The results are compared with those obtained by using [(R,R)-Diop-dbp]PtCl2 (2; Diop-dbp is [(2,2-dimethyl-1,3-dioxolane-4,5-diyl)bis(methylene)]bis(5H-benzo[b]phosphindole)) as the catalyst precursor and with those already published obtained with [(R,R)-Diop]PtCl2 (1; Diop is [(2,2-dimethyl-1,3-dioxolane-4,5-diyl)bis(methylene)]bis(diphenylphosphine)). The systems 2 and 4 (which contain the 5H-benzo[b]phosphindole substituents) are characterized by a lower isomerizing activity and by a higher regioselectivity toward the branched isomer than systems 1 and 3 (which contain the bis(diphenylphosphino) substituents).