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Using a recent result by Bonanno [2], we obtain a multiplicity result for the quasilinear elliptic problem $$displaylines{ - Delta_p u + |u|^{p-2}u = lambda f(u) quad hbox{in } Omega, cr | abla u|^{p-2} frac{partial u}{partial u} = mu g(u) quad hbox{on } partialOmega, }$$ where $Omega$ is a bounded domain in $mathbb R^N$, $N geq 3$ with smooth boundary $partialOmega$, $frac{partial}{partial u}$ is the outer unit normal derivative, the functions $f, g$ are $(p-1)$-sublinear at infinity ($1<p<N$), $lambda$ and $mu$ are positive parameters.