Hi, It is known that the double commutant of the CCR algebra in it's GNS space with respect to some quasifree states are always type III factors. My question is; Will some of them be hyperfinite factors?

Yes, ArakiWoods showed they're always ITPFI factors and ITPFI factors are hyperfinite. See the following: ArakiWoods, A classification of factors It's a bit of a monster paper, the stuff on CCR algebras is near the end. 

