Invar and Elinvar alloys are widely applied for precision measurement instruments. These practical alloys are all ferromagnetic, and the ferromagnetism of these alloys often limits the scope of their application. In recent years, therefore, a considerable amount of efforts are devoted to the research and development for nonferromagnetic Invar or Elinvar alloys.Cr is an antiferromagnetic metal and its magnetic properties can be explained by the SDW theory. The physical properties such as thermal expansivity and electrical resistivity change anomalously near the Ne´el temperature, and these properties are sensibly modified by the addition of other elements.Taking the above‐mentioned results into consideration, present authors investigated the temperature dependences of the physical properties for some Cr‐base primary solid solution alloys, and found these alloys have a certain temperature region in which both Invar and Elinvar characteristics coexist.It is the first time that these both characteristics have been found in the same alloys. And these alloys are practically free from the effect of any magnetic field.