  The quantum hydrodynamic model of the electrostatic waves in the two parallel
layers of two dimensional electron gases (2DEGs) is developed. It is considered
for two regimes: classic regime and quantum regime with the separate spin
evolution. Two Langmuir-like waves are found in classic case which have an
interference-like pattern in the frequency dependence on concentration
$\omega^{2}\sim(n_{01}+n_{02}\pm2\sqrt{n_{01}n_{02}})$. They appear instead of
two 2D Langmuir waves in noninteracting 2DEGs. The spectrum of four waves is
found in the quantum regime. Two extra waves are related to the separate spin
evolution and associated to the spin-electron acoustic waves. The influence of
the quantum Bohm potential is considered either.
