  This short paper presents characterisations of normal arc-transitive
circulants and arc-transitive normal circulants, that is, for a connected
arc-transitive circulant $\Gamma=\Cay(C,S)$, it is shown that 1. Aut(C,S) is
transitive on S if and only if each element of S has order n; 2. $Aut\Gamma\rhd
C$ if and only if S does not contain a coset of any subgroup.
  This completes the classification of arc-transitive circulants given by
Li-Xia-Zhou.
