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Let 
$l\in \mathbb {N}_{\ge 1}$ and 
$\alpha : \mathbb {Z}^l\rightarrow \text {Aut}(\mathscr {N})$ be an action of 
$\mathbb {Z}^l$ by automorphisms on a compact nilmanifold 
$\mathscr{N}$. We assume the action of every 
$\alpha (z)$ is ergodic for 
$z\in \mathbb {Z}^l\smallsetminus \{0\}$ and show that 
$\alpha $ satisfies exponential n-mixing for any integer 
$n\geq 2$. This extends the results of Gorodnik and Spatzier [Mixing properties of commuting nilmanifold automorphisms. Acta Math. 215 (2015), 127–159].
