  We show that under the operation of parity the {\it front-form} $(1/2,\,0)$
and $(0,\,1/2)$ Weyl spinors (massive or massless) do not get interchanged.
This has the important consequence that if a front-form theory containing
$(1/2,\,0)\oplus(0,\,1/2)$ representation space has to be parity covariant then
one must study the evolution of a physical system not only along $x^+$ but also
along the $x^-$ direction. As a result of our analysis, we find an indication
that there may be no halving of the degrees of freedom in the front form of
field theories.
