  A manifestation of electron-hole pairing in nonlinear electromagnetic
response of a double layer graphene system is studied. It is shown that the
pairing causes the appearance of a number of peaks in the frequency dependence
of the intensity of the third harmonic generation (THG). The highest peak
corresponds to \hbar\omega = (2/3)\Delta, where \omega\ is the incident wave
frequency, and \Delta\ is the order parameter of the electron-hole pairing. The
absolute value of the THG intensity in the systems with electron-hole pairing
is in several orders of magnitude greater than the THG intensity in the
unpaired state. It is shown that huge enhancement of the THG intensity occurs
both in the double monolayer and double bilayer graphene systems.
