  We have calculated the crystal electric field of TmTe (T>T_Q) and have
obtained that the ground state of a Tm 4f hole is the $\Gamma_7$ doublet in
agreement with Mossbauer experiments. We study the quadrupole interactions
arising from quantum transitions of 4f holes of Tm. An effective attraction is
found at the L point of the Brillouin zone, $\vec{q}_L$. Assuming that the
quadrupolar condensation involves a single arm of $\vec{q}_L$ we show that
there are two variants for quadrupole ordering which are described by the space
groups C2/c and C2/m. The Landau free energy is derived in mean-field theory.
The phase transition is of second order. The corresponding quadrupole order
parameters are combinations of $T_{2g}$ and $E_g$ components. The obtained
domain structure is in agreement with observations from neutron diffraction
studies for TmTe. Calculated lattice distortions are found to be different for
the two variants of quadrupole ordering. We suggest to measure lattice
displacements in order to discriminate between those two structures.
