Abstract: The FIR spectrum of optically Pumped gaseous molecules was studied theoretically. The signal flow graph was used to solve the density matrix equations of the system assuming that. 1) the molecule interacting with the incident signal (including the pump and detecting signal) was considered to be a six-level quantum system; 2) the pumping power was much larger than the FIR probing signal. A set of analytical solution of the spectral characteristics of-the activated molecules has been obtained. The AC Stark effect of the FIR spectrum of vibrational ground state of activated molecules was demonstrated.The theoretical AC Stark splittings of both the laser lines and absorption spectral lines were in good agreement with the result obtained by C.H.Townes in 1955. A special transition between absorption and emission parts of the characteristic curve was found. The value of AC Stark splitting equals 2Bp/n,where n is the number of FIR photon in the multiphoton process.