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We have investimated the effect of the isospin 1/2, J^P = 0^+ resonant stateK^*_0(1950) on the decays D^0 ->\bar{K}^{0}\eta and D^0 ->\bar{K}^0 \eta' as afunction of the branching ratio sum r =Br(K^*_0(1950)->\bar{K}^0\eta)+Br(K^*_0(1950)->\bar{K}^0 \eta' and coupling constants g_{K^*_0\bar{K}^0\eta},g_{K^*_0\bar{K}^0\eta'}. We have used a factorized input for D^0 -> K^*_0(1950)weak transition through a \pi K loop. We estimated both on- and off-shellcontributions from the loop. Our calculation shows that the off-shell effectsare significant. For $r\geq 30%$ a fit to the decay amplitude A(D^0 ->\bar{K}^0 \eta') was possible, but the amplitude A(D^0 ->\bar{K}^0 \eta)remained at its factorized value. For small values of r, $r\leq 18 %$, we wereable to fit A(D^0 -> \bar{K}^0 \eta), and despite the fact that A(D^0 ->\bar{K}^0 \eta') could be raised by almost 100 % over its factorized value, itstill falls short of its experimental value. A simultaneous fit to bothamplitudes A(D^0 -> \bar{K}^0 \eta') and A(D^0 -> \bar{K}^0 \eta) was notpossible. We have also determined the strong phase of the resonant amplitudesfor both decays.  PACS numbers:13.25.Ft, 13.25.-k, 14.40.LbComment: 16 pages, 6 figures, 3 table

RESONANT FINAL-STATE INTERACTIONS IN $D^0\rightarrow{\bar K}^0\eta,~{\bar K}^0\eta^\prime$ DECAYS