The most important features of Pb1-xMnxTe(In) solid solutions are the effect of Fermi level (FL) pinning and the existence of metastable electronic states resulting in the appearance of the relaxation processes of long duration. The increase of MnTe content in Pb1-xMnxTe(In) leads to the shift of pinned FL towards the conduction band edge E-c and metal-dielectric transition at X similar to 0.05. The kinetic processes under the radiation of Pb1-xMnxTe(In) single crystals (0<X<0.11) have been investigated in the temperature range 4.2-35 K. It has been found that under the composition X variation the view of kinetic curves changes qualitatively. At X less than or equal to 0.07 (T=4.2K) after the light source is switched off the persistent photoconductivity takes place. The subsequent increase of X value results in appearance of a relatively fast relaxation region at the beginning of the kinetic process which transforms into persistent photoconductivity at the tail of the relaxation. The quantity of the electrons participating in the fast relaxation process rises with X increase. The analysis of experimental data is done in terms of the configuration diagram. The existence of a metastable electronic state E-1 of the impurity center together with the ground one E-2 is assumed. It is shown, that if the shift of E-1 and E-2 levels relatively to E-c is characterized by the linear dependence on X, the fast relaxation appears near the point when E-1 level crosses E-c and enters the energy gap.