It is shown that the magnetodipole radiation from the rotating magnetized neutron star must penetrate into its conducting crust. The solution for the magnetodipole and electroquadrupole radiations known as Deusch solution takes place only when the conductivity of the neutron star matter is equal to infinity. For the finite conductivity the solution of the electrodynamic equations is the wave propagating from the neutron star surface to the core where the electric field in rotating frame is not equal to zero. Such electric field excites the electric currents and the tangential magnetic field of the large amplitude. This physics explains the phenomena of Anomalous X-ray Pulsars (AXP) and Magnetars. It can be applied also to the Soft gamma-ray Repeaters (SGR) considering them as the class of AXP when the large Amper forces results to the crash of the crust.