  In this paper, we introduce homogeneous mixed Herz-Morrey spaces
$M\dot{K}_{p,\vec{q}}^{\alpha,\lambda}(\mathbb{R}^n)$ and show it's some
properties. Firstly, the boundedness of sublinear operators, fractional type
operators in homogeneous mixed Herz-Morrey spaces is investigated. In
particular, the above results are still valid for Calder$\acute{o}$n-Zygmund
operators and fractional maximal operators. Lastly, the boundedness of their
commutators in homogeneous mixed Herz-Morrey spaces is obtained.
