<p style='text-indent:20px;'>This work establishes local existence and uniqueness as well as blow-up criteria for solutions <inline-formula><tex-math id="M1">\begin{document}$ (u,b)(x,t) $\end{document}</tex-math></inline-formula> of the Magneto–Hydrodynamic equations in Sobolev–Gevrey spaces <inline-formula><tex-math id="M2">\begin{document}$ \dot{H}^s_{a,\sigma}(\mathbb{R}^3) $\end{document}</tex-math></inline-formula>. More precisely, we prove that there is a time <inline-formula><tex-math id="M3">\begin{document}$ T>0 $\end{document}</tex-math></inline-formula> such that <inline-formula><tex-math id="M4">\begin{document}$ (u,b)\in C([0,T];\dot{H}_{a,\sigma}^s(\mathbb{R}^3)) $\end{document}</tex-math></inline-formula> for <inline-formula><tex-math id="M5">\begin{document}$ a>0, \sigma\geq1 $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M6">\begin{document}$ \frac{1}{2}<s<\frac{3}{2} $\end{document}</tex-math></inline-formula>. If the maximal time interval of existence is finite, <inline-formula><tex-math id="M7">\begin{document}$ 0\leq t < T^* $\end{document}</tex-math></inline-formula>, then the blow–up inequality <p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \frac{C_1\exp\{C_2(T^*-t)^{-\frac{1}{3\sigma}}\}\;\;\;\;\;\;\;}{\;\;\;\;(T^*-t)^{q}\;\;\;\;} \;\;\;\;\;\;\;\;\;\;\leq \|(u,b)(t)\|_{\dot{H}_{a,\sigma}^s(\mathbb{R}^3)} \quad \mbox{with}\,\, q = {\frac{2(s\sigma+\sigma_0)+1}{6\sigma}} $\end{document} </tex-math></disp-formula> <p style='text-indent:20px;'>holds for <inline-formula><tex-math id="M8">\begin{document}$ 0\leq t<T^*, \frac{1}{2}<s<\frac{3}{2} $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M9">\begin{document}$ a>0 $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M10">\begin{document}$ \sigma> 1 $\end{document}</tex-math></inline-formula> (<inline-formula><tex-math id="M11">\begin{document}$ 2\sigma_0 $\end{document}</tex-math></inline-formula> is the integer part of <inline-formula><tex-math id="M12">\begin{document}$ 2\sigma $\end{document}</tex-math></inline-formula>).