  In this article we study the global regularity of 2D generalized
magnetohydrodynamic equations (2D GMHD), in which the dissipation terms are $-
\nu (- \triangle)^{\alpha} u$ and $- \kappa (-\triangle)^{\beta} b$. We show
that smooth solutions are global in the following three cases: $\alpha
\geqslant 1 / 2, \beta \geqslant 1$; $0 \leqslant \alpha < 1 / 2, 2 \alpha +
\beta > 2$; $\alpha \geqslant 2, \beta = 0$. We also show that in the inviscid
case $\nu = 0$, if $\beta > 1$, then smooth solutions are global as long as the
direction of the magnetic field remains smooth enough.
