  The impact of electron-hole pairing on the spectrum of plasma excitations in
double layer systems is investigated. The theory is developed with reference to
a double monolayer graphene. Taking into account the coupling of scalar
potential oscillations with oscillations of the order parameter $\Delta$, we
show that the spectrum of antisymmetric (acoustic) plasma excitations contains
two modes: a weakly damped mode below the gap $2\Delta$ and a strongly damped
mode above the gap. The lower mode can be interpreted as an analog of the
Carlson-Goldman mode. This mode has an acoustic dispersion relation at small
wave vectors and it saturates at the level $2\Delta$ at large wave vectors. Its
velocity is larger than the velocity of the Anderson-Bogoliubov mode
$v_{AB}=v_F$/$\sqrt{2}$, and it can be smaller than the Fermi velocity $v_F$.
The damping rate of this mode strongly increases under increase of temperature.
Out-of-phase oscillations of two order parameters in two spin subsystems are
also considered. This part of the spectrum contains two more modes. One of them
is interpreted as an analog of the Anderson-Bogoliubov (phase) mode and the
other, as an analog of the Schmid (amplitude) mode. With minor modifications
the theory can be extended to describe collective modes in a double bilayer
graphene as well.
