  Motivated by the recent work of Bownik and Ross \cite{BR}, and Jakobsen and
Lemvig \cite{JL}, this article generalizes latest results on reproducing
formulas for generalized translation invariant (GTI) systems to the setting of
super-spaces over a second countable locally compact abelian (LCA) group $G$.
To do so, we introduce the notion of a super-GTI system with finite sequences
as generators from a super-space $L^2(G) \oplus \cdots \oplus L^2(G) $ ($N$
summands). We characterize the generators of two super-GTI systems in the
super-space such that they form a super-dual frame pair. For this, we first
give necessary and sufficient conditions for two Bessel families to be
orthogonal frames (we call as GTI-orthogonal frame systems) when the Bessel
families have the form of GTI systems in $L^2(G)$. As a consequence, we deduce
similar results for several function systems including the case of TI systems,
and GTI systems on compact abelian groups. As an application, we apply our
duality result for super-GTI systems to the Bessel families with a wave-packet
structure (combination of wavelet as well as Gabor structure), and hence a
characterization for dual super wave-packet systems on LCA groups is obtained.
In addition, we relate the well established theory from literature with our
results by observing several deductions in context of wavelet and Gabor systems
over LCA groups with $G=\mathbb{R}^d,\mathbb{Z}^d$, etc.
