  CP violating effects in the single top quark production via flavour changing
neutral current (FCNC) reactions $e^+e^- ->t bar{q}$ and $e^+e^- ->bar{t}q$
(here $q$ refers to charm and up quarks) are studied. The effective Lagrangian
description of the FCNC interactions is used. A numerical analysis is performed
for some next linear colliders. CP violating asymmetries for the number of $q$
and $\bar{q}$ quarks are obtained to be of order $10^{-2}-10^{-3}$ depending on
the CM energy.
