  In this work we analyze the behavior of the spectrum of the peridynamic
fractional $p$-Laplacian, $(-\Delta_p)_{\delta}^s$, under the limit process
$\delta\to0^+$ or $\delta\to+\infty$. We prove spectral convergence to the
classical $p$-Laplacian under a suitable scaling as $\delta\to0^+$ and to the
fractional $p$-Laplacian as $\delta\to+\infty$.
