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

Reduced free products of unital AH algebras and Blackadar and Kirchberg's MF algebras