  AR Scorpii is a close binary system containing a rotation powered white dwarf
and a low mass M type companion star. This system shows non-thermal emission
extending up to the X-ray energy range. We consider hybrid (lepto-hadronic) and
pure hadronic models for the high energy non-thermal processes in this binary
system. Relativistic electrons and hadrons are assumed to be accelerated in a
strongly magnetised, turbulent region formed in collision of a rotating white
dwarf magnetosphere and a magnetosphere/dense atmosphere of the M dwarf star.
We propose that the non-thermal X-ray emission is produced either by the
primary electrons or the secondary $e^\pm$ pairs from decay of charged pions
created in collisions of hadrons with the companion star atmosphere. We show
that the accompanying $\gamma$-ray emission from decay of neutral pions, that
are produced by these same protons, is expected to be on the detectability
level of the present and/or the future satellite and Cherenkov telescopes. The
$\gamma$-ray observations of the binary system AR Sco should allow to constrain
the efficiency of hadron and electron acceleration and also the details of the
radiation processes.
