  In this paper we introduce and investigate the concept of reproducing pairs
which generalizes continuous frames. We will introduce a concept that
represents a unifying way to look at certain continuous frames (resp.
reproducing pairs) on LCA groups, which can be described as continuous
nonstationary Gabor systems and investigate conditions for these systems to
form a continuous frame (resp. reproducing pair). As a byproduct we identify
the structure of the frame operator (resp. resolution operator). Moreover, we
ask the question, whether there always exist mutually dual systems with the
same structure such that the resolution operator is given by the identity, i.e.
given $A:X\rightarrow B(\mathcal{H})$, if there exist
$\psi,\varphi\in\mathcal{H}$, s.t. \begin{equation*}
  f=\int_X \langle f,A(x)\psi\rangle A(x)\varphi d\mu(x),\ \ \forall f\in
\mathcal{H} \end{equation*} and show that the answer is not affirmative. As a
counterexample we use a system generated by a unitary action of a subset of the
affine Weyl-Heisenberg group in $L^2(\mathbb{R})$.
