The methods of electron microscopy, resistometry and magnetometry are used to study ten (36-38)Co - (32-36)Ni - (27-30)Al (at. %) alloys. Cast coarse-crystalline and microcrystalline alloys made by melt spinning in a helium atmosphere are considered. It is shown that the martensite start temperature Ms becomes 30-50°C lower as grains are refined to 1 m m. Replacement of 1 at. % cobalt by nickel and 1 at. % aluminum by nickel makes the temperature interval of the В2«L10 martensite transformation (30-60)°C and (100-110)°C higher respectively. The martensite transformation hysteresis is about 100 degrees. The melt-spun Co38Ni34Al28 alloy with the transformation temperatures Мs = 31°С, Мf = –34°С, Аs = –6°С, Аf = 70°С and Тс = 98°С is a material possessing the magnetically controlled shape memory effect.