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Effect of the axial crystal field in quasioctahedral high-spin Co(II) complexes on the rates of direct one-phonon relaxation processes is discussed. In the framework of this study, the electron-vibrational interaction of the ground orbital triplet 4T1 with Е and T2- vibrations of the octahedral complex, as well as with the rotational modes of T1 symmetry is taken into account. The rates of one-phonon transitions between the Zeeman components of the ground Kramers doublets are shown to decrease by several orders of magnitude with the increase of the absolute value of the axial crystal 1field splitting |∆ax|| from 0 to 1500 cm-1 . This effect is shown to be almost independent of the singn of ∆ax|. These findings seem to be important for rational design of field of the sign of axinduced single ion magnets based on quasioctahedral Co(II) complexes.