In the paper, we prove that reduced free products of unital AH algebras with
respect to given faithful tracial states, in the sense of Voiculescu, are
Blackadar and Kirhcberg's MF algebras. We also show that the reduced free
products of unital AH algebras with respect to given faithful tracial states,
under mild conditions, are not quasidiagonal. Therefore we conclude, for a
large class of AH algebras, the Brown-Douglas-Fillmore extension semigroups of
the reduced free products of these AH algebras with respect to given faithful
tracial states are not groups. Our result is based on Haagerup and
Thorbj{\o}rsen's work on the reduced C$^*$-algebras of free groups.
