Starting with the idea that indium creates a narrow impurity band of q
uasi-local resonant states in the valence band of the SnTe-GeTe system
, we have noticed that superconductivity with T-c>0.4 K in these mater
ials requires not only partial electron occupation of the resonant sta
tes pinning the Fermi level, but also the following additional conditi
on: on the energy scale the band of resonant impurity states should ov
erlap additional valence band states with a high density of states. An
analysis of a correlation between the experimental data of the resist
ivity, the Hall concentration and superconducting properties was made
for solid solutions of GezSn1-xTe:In (0 less than or equal to z less t
han or equal to 0.4; In: 5 and 16 at.%). It was found that the superco
nducting parameters (T-c, H-c2(O)) have a bell-shaped function of the
Ge content, revealing a maximum near the edge of the heavy-hole valenc
e band.