[en] The magnetohydrodynamic stability of an annular liquid jet, concentric with a solid cylinder as a mantle, and acting upon it through capillarity, electromagnetic (with varying magnetic field) and inertia forces, is discussed. An eigenvalue relation, valid to all nonaxisymmetric and axisymmetric disturbances, is derived and studied analytically and the results are confirmed numerically. The model is capillary unstable only to small axisymmetric disturbances whose wavelengths are longer than the annular jet circumference and stable to all other disturbances. The magnetic field inside the jet is stabilizing in all disturbances for all wavelengths and easily suppressing the capillary instability. The vacuum tangential varying magnetic field is destabilizing to the axisymmetric mode for all wavelengths, while to nonaxisymmetric modes it is stabilizing or destabilizing according to restrictions. The required restrictions for suppressing the capillary instability by the electromagnetic force are identified. The analytical stability results are confirmed numerically utilizing the stability criteria in the computer simulation for different values of the problem parameters