The temperature T dependence of the magnetic susceptibility chi and electrical resistivity rho of gamma -Fe-31 at.% Mn alloys containing 2-8.7 at.% Ge and 5.2 at.% Cr were measured in detail over the temperature range 5-500 K. The Neel transition of these alloys accompanied by an anomalous change in rho has been observed at a temperature of 300-430 K. In lowering the temperature to about 5 K, no second resistivity anomaly for gamma -Fe-31 at.% Mn or gamma -Fe-31 at.% Mn-5.2 at.% Cr alloys was found, but a secondary resistivity minimum was observed below 50 K in the gamma -Fe-31 at.% Mn-Ge alloys. The resistivity minimum temperature T_min increases in proportion to the Ge concentration, and the resistivity measured from T_min to about 5 K of the Fe-Mn-Ge alloys can be plotted as a linear function of log T, T² and square root T. These results suggest that the resistivity minimum in antiferromagnetic gamma -Fe-Mn-Ge alloys is due to a Kondo-like effect caused by localized magnetic moments on Fe atom sites which are induced or enhanced by the solution of Ge in gamma -Fe-Mn alloys.