The time-dependent coupled equations of reaction processes are solved by means of the Green's functions of their stationary parts. It is pointed out that the yields of nuclear reac tions (time spectra) become the function of time and the characteristic parameters of the phase of compound nucleus having dimension of time: the number of degrees of freedom of motion, the Poincare cycle, the delay, the relaxation time and the lifetime. Under the strong correlation condition for the transition matrix elements, the solution of time-dependent coupled equations satisfies the master equation of irreversible process inside the compound nucleus given by the statistical mechanics. An example of the time spectrum for a two-step reaction is shown. § I. Introduction Existence of the irreversible process in nuclear reactions has been studied by means of the time-dependent perturbation, D the statistical treatments2), 3) and recently the pre-equilibrium modeL''·'' It has been shown experimentally that the reaction times of the direct interactions6' and the compound nucleus processes7' are about 10- 21 sec and 10-16 sec, respectively. It was also pointed out by a previous paper8 ' that the reaction steps (phase of compound nucleus) inside the compound nucleus were able to be lined sequentially starting from the simplest phase and ending in the most complex one of compound nucleus. The number of matrix elements for the transition from a state in the simple phase of compound nucleus to states in the complex one will be much larger than those from a state in the complex one to states in the simple one, because the level density of the former is much smaller than the latter. Then the time dependent coupled equations of each phase8' will be reduced to the master equation after the statistical averaging. 91 The nuclear reaction inside compound nuCleus starts from the simple phase and goes on step by step in the direction of more complex phases and finally reaches the statistical equilibrium of compound nucleus. It is our purpose to solve the time-dependent coupled equations among the phases of compound nucleus and to show the existence of an irreversible process in nuclear reactions. When a wave packet with the shortest time duration comes into a target nucleus, the fastest outgoing wave packet will be the direct reflection from the nuclear surface with zero delay; then many outgoing wave packets going through the n-phases of compound nucleus will come out of it in order of the