  In this paper, we prove the asymptotic stability of Couette flow in a strong
uniform magnetic field for the Euler-MHD system, when the perturbations are in
Gevrey-$\frac{1}{s}$, $(\frac12<s\leq 1)$ and of size smaller than the
resistivity coefficient $\mu$. More precisely, we prove (1) the
$\mu^{-\frac13}$-amplification of the perturbed vorticity, namely, the size of
the vorticity grows from
$\|\omega_{\mathrm{in}}\|_{\mathcal{G}^{\lambda_{0}}}\lesssim \mu$ to
$\|\omega_{\infty}\|_{\mathcal{G}^{\lambda'}}\lesssim \mu^{\frac23}$; (2) the
polynomial decay of the perturbed current density, namely,
$\left\|j_{\neq}\right\|_{L^2}\lesssim \frac{c_0 }{\langle t\rangle^2
}\min\left\{\mu^{-\frac13},\langle t \rangle\right\}$; (3) and the damping for
the perturbed velocity and magnetic field, namely, \[
\left\|(u^1_{\neq},b^1_{\neq})\right\|_{L^2}\lesssim \frac{c_0\mu }{\langle
t\rangle }\min\left\{\mu^{-\frac13},\langle t \rangle\right\}, \quad
\left\|(u^2,b^2)\right\|_{L^2}\lesssim \frac{c_0\mu }{\langle t\rangle^2
}\min\left\{\mu^{-\frac13},\langle t \rangle\right\}. \] We also confirm that
the strong uniform magnetic field stabilizes the Euler-MHD system near Couette
flow.
