  We investigate some processes of the associated production of a neutral
top-pion $\Pi^{0}_{t}$ with a pair of fermions($e^{+}e^{-}\to
f\bar{f}\Pi^{0}_{t}$) in the context of top-color-assisted technicolor(TC2)
theory at future $e^{+}e^{-}$ colliders.
  The studies show that the largest cross sections of the processes
$e^{+}e^{-}\to f'\bar{f'}\Pi^{0}_{t}(f'=u,d,c,s,\mu,\tau)$ could only reach the
level of 0.01fb, we can hardly detect a neutral top-pion through these
processes. For the processes $e^{+}e^{-}\to e^{+}e^{-}\Pi^{0}_{t}$,
$e^{+}e^{-}\to t\bar{t}\Pi^{0}_{t}$ and $e^{+}e^{-}\to b\bar{b}\Pi^{0}_{t}$,
the cross sections of these processes are at the level of a few fb for the
favorable parameters and a few tens, even hundreds, of neutral top-pion events
can be produced at future $e^{+}e^{-}$ colliders each year through these
processes. With the clean background of the flavor-changing $t\bar{c}$ channel,
the top-pion events can possibly be detected at the planned high luminosity
$e^{+}e^{-}$ colliders. Therefore, such neutral top-pion production processes
provide a useful way to detect a neutral top-pion and test the TC2 model
directly.
