The Pair Approximation method is applied to studies of the bilayer and multilayer magnetic systems with simple cubic structure. The method allows to take into account quantum effects related with non-Ising couplings. The paper adopts the anisotropic Heisenberg model for spin S = 1/2 and considers the phase transition temperatures as a function of the exchange integrals strength in line with the role of intra-and interplanar anisotropic interactions in the onset of low-dimensional magnetism. The compensation effect for the Curie temperature is found for asymmetric interactions within the neighbouring planes of the bilayer system. The paper predicts the saturation of the Curie temperature for strong interplanar interactions. However, such an effect for the multilayer system occurs only when the interplanar interactions are of purely isotropic character. Figure 1: (a) A schematic view of the bilayer composed of two layers, A and B. The intraplanar couplings are J AA x = J AA y = J AA ⊥ , J AA z and J BB x = J BB y = J BB ⊥ , J BB z , respectively. The interplanar coupling is J AB x = J AB y = J AB ⊥ , J AB z . (b) A schematic view of a multilayer, containing an infinite number of subsequent layers A and B.visible in Fig. 8 (b) this reduction of T c becomes less pronounced for the increasing coupling in the B plane. On the other hand, when J BB z is comparable with J AA z the behaviour of the critical temperature follows the trend presented in the Fig. 8(a). It is particularly interesting that at some value of J BB z /J AA z the critical temperature k B T c /J AA z = 1/2 ln 2 is restored for each curve, even though the disordering Heisenberg interplanar couplings are present. The value of J BB z /J AA z at which the compensation of the opposite influences of J AB ⊥ and J BB z takes place is very weakly sensitive to the strength of interplanar coupling. This is visible in the Fig. 8 (b) as an approximate interception point of all the curves plotted for various values of J AB z /J AA z . The insensitivity of the coupling ratio J BB z /J AA z * , for which T c has the constant value (characteristic of an uncoupled bilayer system), on the interplanar interaction is further illustrated in the Fig. 9. There, the values of J BB z /J AA z * are plotted as a function of the interplanar coupling J AB z /J AA z strength. The plot is prepared not only for isotropic