A glass-fibre communications system using travelling-wave amplifiers operating on the laser principle is studied. The propagation characteristics of such a system are investigated theoretically with the aid of the mean value and variance of the statistical distribution of the number of photons. When linear optical amplifiers are used, the noise increases at each stage on account of spontaneous emission in the amplifier, thereby limiting the length of the transmission range. The maximum transmission range increases with the magnitude of the input signal and decreases with the gain per stage and the number modes.