Twenty magnetic Chemically Peculiar (CP2) stars of the SrCrEu subgroup mostly brighter than the 7.5 visual magnitude have been investigated in the near infrared at 1.25, 1.6 and 2.2 mu . The stars HD 3980, HD 24712, HD 49976, HD 83368, HD 96616, HD 98088, HD 118022, HD 125248, HD 148898, HD 203006, and HD 220825 have been found to be variable in the infrared with the same period as the visible light, spectrum, and magnetic field variations. HD 221760 is also variable with a period of 12.45 days, which has to be confirmed. The stars HD 72968, HD 111133, HD 126515, HD 153882, and HD 164258 do show some hint of variability, although the data are too few. Infrared variability has been detected for the first time in the stars HD 101065, and HD 206088, which have not yet been considered as variable. No variability has been detected for the star HD 137949 within a time scale of the order of ten days. Based on observations collected at the European Southern Observatory, La Silla Chile.