We study the influence of the anisotropy of the Frank elastic constants on the magnetic reorientation of the nematic phase of polymer liquid crystals. In the magnetic reorientation following a 90' director rotation with respect to an aligning magnetic field, a pattern of inversion walls develops which depends on the relative magnitude of the elastic constants and the magnetic coherence length. We show how this dependence can be experimentally studied by proton NMR. The transition from a homogeneous director reorientation to a distorted director reorientation is theoretically studied as a function of the rotation angle α A critical angle of rotation ac shows up, and we study its dependence on the anisotropies K3/K1 and K3/K2. Depending on these ratios and on the wavelength of the distortion, critical angles 45" < αc, < 90" are predicted for materials with positive anisotropy of the magnetic susceptibility xa and 0º < αc < 45º (mod π/2) for materials with xa < 0. Within the frame of a phase transition analogy, a Landau-like theory predicts the transition to be second order.