Two-photon lasers and laser amplifiers are studied by using the rate equations. The steady solution is obtained and its stability is analysed. The time evolution of large deviation from the steady solution is studied by using computer simulation. The population inversion and the trigger input must exceed certain thresholds to operate a two-photon laser. The method for producing giant-pulse is discussed. The possibility of building a pratioal two-photon laser is analysed basing on the known data, A Doppler-free two-photon laser needs much lower threshold but much more serious frequency matching among the atom system, cavity and the trigger input. Such a Doppler-free two-photon laser could find applications in laser spectroscopy and in the accurate metrology. Two-photon laser amplifiers distort the input waveform seriously. This distortion depends strongly on the input intensity.