General patterns of the sensitivity of embryos to hypothermia are described, such as its species-specific dependence, its relationship with the embryonic stage, etc. Data are provided on differences in the cold resistance of the inner cell mass and trophectoderm cells, as well as that of the nucleus and cytoplasm. The mechanisms underlying the effects of cold on mammalian eggs and embryos are considered, and ways of improving the method of hypothermic storage are discussed. The general technological principles of the storage of mammalian embryos at positive near-zero temperatures are formulated for the first time. Advantages and drawbacks of the method and its possible practical application are discussed.