This work reports a theoretical study on the linear threshold of static director distortions in a rigidly anchored nematic sample subjected to the simultaneous actions of electric (E) and magnetic (B) fields applied along certain symmetry directions with respect to the initial uniform director alignment a,. The results mainly concern a material having susceptibility anisotropies of opposite signs (epsilon(A) > 0, chi(A) < 0). The deformation above the electric threshold may be homogeneous (HD) or periodic (PD) depending upon material and geometric parameters. PD is quenched when n(0) is tilted sufficiently away from the homeotropic or when B is impressed away from E. For a given director pretilt, the direction of post threshold periodicity changes continuously with the magnetic tilt. At a given magnetic tilt, the PD threshold parameters exhibit a discontinuous change when the director pretilt is varied. Phase diagrams in different planes of the parameter space demarcate the regions of existence of PD and HD. The importance of elastic anisotropy in determining the nature of PD emerges from a study of a hypothetical material having two equal curvature elastic constants.