  It is shown that a separable C*-algebra is inner quasidiagonal if and only if
it has a separating family of quasidiagonal irreducible representations. As a
consequence, a separable C*-algebra is a strong NF algebra if and only if it is
nuclear and has a separating family of quasidiagonal irreducible
representations. We also obtain some permanence properties of the class of
inner quasidiagonal C*-algebras.
