Using the continuum theory in the linear perturbation limit, the formation of static periodic distortions (PD) is studied in a planar nematic sample under the action of crossed electric (E) and magnetic (H) fields. In a nematic dielectric with positive dielectric and diamagnetic anisotropies (epsilon A > 0, chi A > 0), the wave vector of H induced PD depends on the tilt of H in a plane normal to the initial director orientation n o when E is in the sample plane; change of magnetic tilt may cause discontinuous changes in the wave vector. Similar results are obtained when electrical conductivity is taken into account with hydrodynamic effects being assumed absent. Calculations are extended to a study of PD in nematics with high elastic anisotropy for different signs of epsilon A and chi A. When such materials have susceptibility anisotropies of opposite sign, change in magnetic tilt may cause 're-entrant' appearances of distortions. When anchoring is weak enough, the saddle-splay elastic constant K 24 can influence the domain of existence of PD. Possible effects of flexoelectricity as well as results for cylindrical geometry are qualitatively discussed.