  The goal of this article is to present the graded weakly $S$-primary ideals
and $g$-weakly $S$-primary ideals which are extensions of graded weakly primary
ideals. Let $R$ be a commutative graded ring, $S\subseteq h(R)$ and $P$ be a
graded ideal of $R$. We state $P$ is a graded weakly $S$-primary ideal of $R$
if there exists $s\in S$ such that for all $x,y \in h(R)$, if $0\neq xy\in P$,
then $sx\in P$ or $sy\in Grad(P)$ (the graded radical of $P$). Several
properties and characteristics of graded weakly $S$-primary ideals as well as
graded $g$-weakly $S$-primary ideals are investigated.
