  We show that the gap between the two greatest eigenvalues of the generalised
Petersen graphs $P(n,k)$ tends to zero as $n \rightarrow \infty$. Moreover, we
provide explicit upper bounds on the size of this gap. It follows that these
graphs have poor expansion properties for large values of $n$. We also show
that a positive proportion of the eigenvalues of $P(n,k)$ tend to the valency.
