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              <p>We prove central and non-central limit theorems for the Hermite variations of the anisotropic fractional Brownian sheet $W^{\alpha, \beta}$ with Hurst parameter $(\alpha, \beta) \in (0,1)^2$. When $0&lt;\alpha \leq 1-\frac{1}{2q}$ or $0&lt;\beta \leq 1-\frac{1}{2q}$ a central limit theorem holds for the renormalized Hermite variations of order $q\geq 2$, while for $1-\frac{1}{2q}&lt;\alpha, \beta &lt; 1$ we prove that these variations satisfy a non-central limit theorem. In fact, they converge to a random variable which is the value of a two-parameter Hermite process at time $(1,1)$.</p>
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