  We prove quasiminimality of the regular mixed Tsirelson spaces
T[(S_n,\theta_n)_n] with the sequence (\frac{\theta_n}{\theta^n})_n decreasing,
where \theta=\lim_n \theta_n^{1/n}, and quasiminimality of all mixed Tsirelson
spaces T[(A_n,\theta_n)_n]. We prove that under certain assumptions on the
sequence (\theta_n)_n the dual spaces are quasiminimal.
