  In this paper, we introduce $\phi$-$\delta$-primary elements in a compactly
generated multiplicative lattice $L$ and obtain its characterizations. We prove
many of its properties and investigate the relations between these structures.
By a counter example, it is shown that a $\phi$-$\delta$-primary element of $L$
need not be $\delta$-primary and found conditions under which a
$\phi$-$\delta$-primary element of $L$ is $\delta$-primary.
