  A mass-shift of the axion propagating in an external constant homogenious
magnetic field is calculated. The contributions via an electron loop and a
virtual photon are examined. It is shown that the virtual photon contribution
dominates substantially over the electron-loop one. Under the conditions of the
early Universe the electron-loop contribution to the massless axion mass-shift
is equal to zero while the virtual photon contribution is finite and can be of
order of the recent restrictions on the axion mass.
