The capillary instability of a magnetically anisotropic liquid cylinder and jets, such as Nematic liquid crystals (LC), in magnetic fields, is considered using an energy approach. The boundary problem is solved in the linear approximation of the anisotropy a of the magnetic susceptibility .The effect of the anisotropy, in the region 2 |1 {a^2 } ,can be strong enough to counteract and even reverse the tendency of the field to enhance stabilization by increasing the cut-off wave number ks , beyond the conventional one set by Rayleigh. It is shown that the elastic effect, which is typical of LC, is significant on the scale of nano-jets, where it prevails over the magnetic effect. The jet instability is determined by surface tension, elasticity, and magnetic permeability and anisotropy. The relative influence of the elasticity and permeability on the jet stability depends on its radius . This is particularly true on the nano-scale.