  In 2003, Zudilin presented a $q$-analogue of Euler's identity for one of the
variants of $q$-double zeta function. This article focuses on exploring
identities related to another variant of $q$-double zeta function and its star
variant. Using a $q$-analogue of the Nielsen Reflexion Formula for $q>1$, we
investigate identities involving different versions of $q$-analogues of the
Riemann zeta function and the double-zeta function. Additionally, we analyze
the behavior of $\zeta_q(s_1, s_2)$ as $s_1$ and $s_2$ approach to $0$ and
compare these limits to those of the classical double-zeta function. Finally,
we discuss the $q$-analogue of the Mordell-Tornheim $r$-ple zeta function and
its relation with the $q$-double zeta function.
