  Anticipated backward stochastic differential equations, studied the first
time in 2007, are equations of the following type: {tabular}{rlll} $-dY_t$ &=&
$f(t, Y_t, Z_t, Y_{t+\delta(t)}, Z_{t+\zeta(t)})dt-Z_tdB_t, $ & $ t\in[0, T];$
$Y_t$ &=& $\xi_t, $ & $t\in[T, T+K];$ $Z_t$ &=& $\eta_t, $ & $t\in[T, T+K].$ In
this paper, we give a necessary and sufficient condition under which the
comparison theorem holds for multidimensional anticipated backward stochastic
differential equations with generators independent of the anticipated term of
$Z$.
