A cyclic edge‐cut of a graph G is an edge set, the removal of which separates two cycles. If G has a cyclic edge‐cut, then it is called cyclically separable. For a cyclically separable graph G, the cyclic edge‐connectivity λ
c
(G) is the cardinality of a minimum cyclic edge‐cut of G. We call a graph super cyclically edge‐connected, if the removal of any minimum cyclic edge‐cut results in a component which is a shortest cycle. In this paper, we show that a connected vertex‐transitive or edge‐transitive graph is super cyclically edge‐connected if either G is cubic with girth g(G)≥7, or G has minimum degree δ(G)≥4 and girth g(G)≥6.
