  We have recently developed a nuclear model, specially designed to describe
double charge exchange (DCE) processes,which is a natural extension of the
$pn$-QRPA model for $\beta$-decay to $\beta\beta$-decay. Ergo, this model, in
addition to including the pairing correlations and having the same number of
free parameters, brings into play the $ppnn$-quasiparticle excitations and the
Pauli Principle, which are essential ingredients to correctly account for the
nuclear matrix elements (NMEs) for $\beta\beta$-decays and nuclear reactions to
all $0^+$ and $2^+$ final states, including resonances, and not just to the
ground state as in $pn$-QRPA. In addition, it allows us to evaluate the
$Q_{\beta\beta}$-values, and the excitation energies in final nucleus, and to
work with a single-particle space large enough for the DCE sum rules to be
satisfied. So far it has been applied to the $2\nu\beta\beta$-decay, and here
we extend it to the $0\nu\beta\beta$-decay. The model that comes closest in
terms of its advantages is the shell model. We describe here the DCE
observables in: i) $^{76}$Se, which have been recently measured in the GERDA
and MAJORANA Experiments, and ii) $^{124}$Te, for which has been reported
recently the first direct observation of $2\nu$ double electron capture with
the XENON1T Dark Matter detector. A good agreement with the data is obtained
for both the ground state and the excited states. We have found that the
reaction and $0\nu\beta\beta$-decay NMEs are of the same order of magnitude
even in the region of giant resonances.
