  The structure of cyclically pure injective modules over a commutative ring
$R$ is investigated and several characterizations for them are presented. In
particular, we prove that a module $D$ is cyclically pure injective if and only
if $D$ is isomorphic to a direct summand of a module of the form $\Hom_R(L,E)$
where $L$ is the direct sum of a family of finitely presented cyclic modules
and $E$ is an injective module. Also, we prove that over a quasi-complete
Noetherian ring $(R,\fm)$ an $R$-module $D$ is cyclically pure injective if and
only if there is a family $\{C_\lambda\}_{\lambda\in \Lambda}$ of cocyclic
modules such that $D$ is isomorphic to a direct summand of $\Pi_{\lambda\in
\Lambda}C_\lambda$. Finally, we show that over a complete local ring every
finitely generated module which has small cofinite irreducibles is cyclically
pure injective.
