  A Cayley Graph for a group $G$ is called normal edge-transitive if it admits
an edge-transitive action of some subgroup of the Holomorph of $G$ (the
normaliser of a regular copy of $G$ in $\operatorname{Sym}(G)$). We complete
the classification of normal edge-transitive Cayley graphs of order a product
of two primes by dealing with Cayley graphs for Frobenius groups of such
orders. We determine the automorphism groups of these graphs, proving in
particular that there is a unique vertex-primitive example, namely the flag
graph of the Fano plane.
