  We have studied theoretically the effect of Electrical Magneto-Chiral
Anisotropy (eMChA) in $p$-type tellurium crystals. It is shown that the terms
$k_i B_j$ in the hole Hamiltonian, linear both in the wave vector ${\mathbf k}$
and the magnetic field ${\mathbf B}$, do not lead to the eMChA and one needs to
include the higher-order terms like $k_i^3 B_j$. Two microscopic mechanisms of
the effect are considered. In the first one only elastic scattering of holes by
impurities or imperfections are taken into consideration only. In the second
mechanism, besides the elastic scattering processes the hole gas heating and
its energy relaxation are taken into account. It is demonstrated that he both
contributions to the magneto-induced rectification are comparable in magnitude.
The calculation is performed by using two independent approaches, namely, in
the time relaxation approximation and in the limit of of small chiral band
parameter $\beta$. A bridge is thrown between the eMChA and magneto-induced
photogalvanic effects.
