  In this paper, we prove the global well-posedness for the three-dimensional
magnetohydrodynamics (MHD) equations with zero viscosity and axisymmetric
initial data. First, we analyze the problem corresponding to the Sobolev
regularities $ H^s\times H^{s-2}$, with $ s>5/2$. Second, we address the same
problem but for the Besov critical regularities $ B_{p,1}^{\frac3p+1}\times
B_{1,p}^{\frac3p-1}$, $1\leq p\leq \infty$. This case turns out to be more
subtle as the Beale-Kato-Majda criterion is not known to be valid for rough
regularities.
