Cross-efficiency　evaluation　is　an　effective　approach　to　ranking　decision　making　units　(DMUs)　that　utilize　multiple　inputs　to　produce　multiple　outputs.　Its　models　can　usually　be　developed　in　a　way　that　is　either　aggressive　or　benevolent　to　other　DMUs,　depending　upon　the　decision　maker　(DM)＇s　subjective　preference　to　the　two　extreme　cases.　This　paper　proposes　several　new　data　envelopment　analysis　(DEA)　models　for　cross-efficiency　evaluation　by　introducing　a　virtual　ideal　DMU　(IDMU)　and　a　virtual　anti-ideal　DMU　(ADMU).　The　new　DEA　models　determine　input　and　output　weights　from　the　point　of　view　of　distance　from　IDMU　or　ADMU　without　the　need　to　be　aggressive　or　benevolent　to　any　DMUs.　As　a　result,　the　cross-efficiencies　measured　by　these　new　DEA　models　are　neutral　and　more　logical.　Numerical　examples　are　provided　to　illustrate　the　potential　applications　of　these　new　DEA　models　and　their　effectiveness　in　ranking　DMUs.　(C)　2011　Elsevier　Ltd.　All　rights　reserved.