The quantum electrodynamical theory of three-photon transitions in hydrogen-like ions is
presented. Emission probabilities of various three-photon decay channels for 2 p 3 2 , 2 p 1 2 and 2 s 1 2 states are calculated forZ,the nuclear chargevalue, 1  Z  95. The results are given in two different gauges. The fully relativistic three-photon decay rates of hydrogen-like ions with half-integer nuclear spin are given for transitions between fine structure components. The results can be applied to the Bose–Einstein statistics tests for multiphoton systems.