  In this paper we prove a Liouville type theorem for the stationary
magnetohydrodynamics(MHD) system in $\Bbb R^3$. Let $(v, B, p)$ be a smooth
solution to the stationary MHD equations in $\Bbb R^3$. We show that if there
exist smooth matrix valued potential functions ${\bf \Phi}$, ${\bf \Psi}$ such
that $ \nabla \cdot {\bf \Phi} =v$ and $\nabla \cdot {\bf \Psi}= B$, whose
$L^6$ mean oscillations have certain growth condition near infinity, namely
$$-\!\!\!\!\!\int_{B(r)} |\mathbf{\Phi} - \mathbf{\Phi}_{ B(r)} |^6 dx +
-\!\!\!\!\!\int_{B(r)} |\mathbf{\Psi}- \mathbf{\Psi}_{ B(r)} |^6 dx\le C r\quad
\forall 1< r< +\infty,$$ then $v=B= 0$ and $p=$constant. With additional
assumption of $$r^{-8}\int_{B(r)}|B-B_{B(r)}|^6dx\to 0\quad \mathrm{as}\quad
r\to+\infty,$$ similar result holds also for the Hall-MHD system.
