A theory of the antiferromagnetism of CuCl22H2O single crystal is developed, basing on the Van Vleck model modified by the introduction of the anisotropic spin-spin coupling besides the usual isotropic exchange coupling. Since the spin quantum number S of the magnetic Cu2+ ion in this substance is 1/2, the effect of the crystalline electric field can only be taken into account by adopting an adequate tensor form for the Lande g-factor. Starting from this point of view, formulas for the anisotropy of the susceptibility, both above and below the Curie point, and for the temperature variation of the anisotropy constant are derived. The critical field discovered by C. J. Gorter et al. and the antiferromagnetic resonance frequency are also discussed.