  We study the dynamic effects in the double graphene-layer (GL) structures
with the resonant-tunneling (RT) and the negative differential inter-GL
conductivity. Using the developed model, which accounts for the excitation of
self-consistent oscillations of the electron and hole densities and the ac
electric field between GLs (plasma oscillations),
  we calculate the admittance of the double-GL RT structures as a function of
the signal frequency and applied voltages, and the spectrum and
increment/decrement of plasma oscillations. Our results show that the
electron-hole plasma in the double-GL RT structures with realistic parameters
is stable with respect to the self-excitation of plasma oscillations and
aperiodic perturbations. The stability of the electron-hole plasma at the bias
voltages corresponding to the inter-GL RT and strong nonlinearity of the RT
current-voltage characteristics enable using the double-GL RT structures for
detection of teraherz (THz) radiation. The excitation of plasma oscillations by
the incoming THz radiation can result in a sharp resonant dependence of
detector responsivity on radiation frequency and the bias voltage. Due to a
strong nonlinearity of the current-voltage characteristics of the double-GL
structures at RT and the resonant excitation of plasma oscillations, the
maximum responsivity, $R_V^{max}$, can markedly exceed the values $(10^4 -
10^5)$~V/W at room temperature.
