This article studies cluster-tilted algebras whose quiver is cyclically
oriented. In this case an explicit description of the defining relations is
given. For this kind of algebras, it is also shown that there exists an
admissible cut and moreover that each arrow of the quiver is contained in an
admissible cut. Furthermore, we show that if the endomorphism ring of an
algebra of global dimension two over its cluster category, in the sense of
Amiot, is cluster-tilted and has a cyclically oriented quiver, then the
original algebra is a quotient by an admissible cut.