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Anticipated backward stochastic differential equations, studied the firsttime 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, $ & $t\in[T, T+K].$ Inthis paper, we give a necessary and sufficient condition under which thecomparison theorem holds for multidimensional anticipated backward stochasticdifferential equations with generators independent of the anticipated term of$Z$.

Necessary and sufficient condition for the comparison theorem of multidimensional anticipated backward stochastic differential equations