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Let $\ell$ denote a non-negative integer. A connected graph $\Gamma$ of even order at least $2\ell+2$ is $\ell$-extendable if it contains a matching of size $\ell$ and if every such matching is contained in a perfect matching of $\Gamma$. A connected regular graph $\Gamma$ is edge-regular, if there exists an integer $\lambda$ such that every pair of adjacent vertices of $\Gamma$ have exactly $\lambda$ common neighbours. In this paper we classify $2$-extendable edge-regular graphs of even orderdoi:10.37236/8073 fatcat:jukerqhj7raz5pnde5jme2w46e