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Let ${𝕄}_n$ be the class of all multiloop algebras of finite dimensional simple Lie algebras relative to $n$-tuples of commuting finite order automorphisms. It is a classical result that ${𝕄}_1$ is the class of all derived algebras modulo their centres of affine Kac-Moody Lie algebras. This combined with the Peterson-Kac conjugacy theorem for affine algebras results in a classification of the algebras in ${𝕄}_1$. In this paper, we classify the algebras in ${𝕄}_2$, and further determine the relationship between ${𝕄}_2$ and two...