  We explore a possibility to explain the phenomenon of the Anomalous X-ray
Pulsars (AXP) and Soft Gamma-ray Repeaters (SGR) within the scenario of
fall-back magnetic accretion onto a young isolated neutron star. The X-ray
emission of the pulsar in this case is originated due to accretion of matter
onto the surface of the neutron star from the magnetic slab surrounding its
magnetosphere. The expected spin-down rate of the neutron star within this
approach is close to the observed value. We show that these neutron stars are
relatively young and are going through a transition from the propeller state to
the accretor state. The pulsars activity in the gamma-rays is connected with
their relative youth and is provided by the energy stored in the
non-equilibrium layer located in the crust of low-mass neutron stars. This
energy can be released due to mixing of matter in the neutron star crust with
super heavy nuclei approaching its surface and getting unstable. The nuclei
fission in the low-density region initiates chain reactions leading to the
nuclear explosion. The outbursts are likely to be triggered by an instability
developing in the region where the matter accreted by the neutron star is
accumulated at the magnetic pole regions.
