Abstract
The group classification of models of axion electrodynamics with arbitrary self-interaction of axionic field is carried out. It is shown that extensions of the basic Poincar\'e invariance of these models appear only for constant and exponential interactions. The related conservation laws are discussed. The maximal continuous symmetries of the 3d Chern-Simons electrodynamics and Carroll-Field-Jackiw electrodynamics are presented. Using the In\"on\"u-Wigner contraction the nonrelativistic limit of equations of axion electrodynamics is found. Exact solutions for the electromagnetic and axion fields are discussed including those which describe propagation with group velocities faster than the speed of light. However these solutions are causal since the corresponding energy velocities are subluminal.
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