  We consider the problem of minimising the $k$th eigenvalue, $k \geq 2$, of
the ($p$-)Laplacian with Robin boundary conditions with respect to all domains
in $\mathbb{R}^N$ of given volume $M$. When $k=2$, we prove that the second
eigenvalue of the $p$-Laplacian is minimised by the domain consisting of the
disjoint union of two balls of equal volume, and that this is the unique domain
with this property. For $p=2$ and $k \geq 3$, we prove that in many cases a
minimiser cannot be independent of the value of the constant $\alpha$ in the
boundary condition, or equivalently of the volume $M$. We obtain similar
results for the Laplacian with generalised Wentzell boundary conditions $\Delta
u + \beta \frac{\partial u}{\partial \nu} + \gamma u = 0$.
