  We study the neutral exciton energy spectrum fine structure and its spin
dephasing in transition metal dichalcogenides such as MoS$_2$. The interaction
of the mechanical exciton with its macroscopic longitudinal electric field is
taken into account. The splitting between the longitudinal and transverse
excitons is calculated by means of the both electrodynamical approach and
$\mathbf k \cdot \mathbf p$ perturbation theory. This long-range exciton
exchange interaction can induce valley polarization decay. The estimated
exciton spin dephasing time is in the picosecond range, in agreement with
available experimental data.
