Summary: We prove that solutions of the anisotropic Allen-Cahn equation in double-obstacle form \[ \varepsilon\partial_t\varphi-\varepsilon\lambda A'(\nabla\varphi)-{1\over\varepsilon} \varphi={\pi\over 4} u\quad\text{in }[|\varphi|<1], \] where \(A\) is a strictly convex function, homogeneous of degree two, converge to an anisotropic mean-curvature flow \(V_n=-\text{tr}(B(N)D^2B(N)R)-B(N)u\), when this equation admits a smooth solution in \(\mathbb{R}^n\). Here, \(V_N\) and \(R\) respectively denote the normal velocity and the second fundamental form of the interface, and \(B:=\sqrt{2A}\). More precisely, we show that the Hausdorff-distance between the zero-level set of \(\varphi\) and the interface of the above anisotropic mean-curvature flow is of order \(O(\varepsilon^2)\).