A search for CP violation in the phase-space structures of D0 and D0bar decays to the final states K-K+pi-pi+ and pi-pi+pi+pi- is presented. The search is carried out with a data set corresponding to an integrated luminosity of 1.0fb^-1 collected in 2011 by the LHCb experiment in $pp$ collisions at a centre-of-mass energy of 7TeV. For the K-K+pi-pi+ final state, the four-body phase space is divided into 32 bins, each bin with approximately 1800 decays. The p-value under the hypothesis of no CP violation is 9.1%, and in no bin is a CP asymmetry greater than 6.5% observed. The phase space of the pi-pi+pi+pi- final state is partitioned into 128 bins, each bin with approximately 2500 decays. The $p$-value under the hypothesis of no CP violation is 41%, and in no bin is a CP asymmetry greater than 5.5% observed. All results are consistent with the hypothesis of no CP violation at the current sensitivity.
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