Two-sided　mergers　and　acquisitions　(M&A)　fits　have　been　regarded　as　a　critical　step,　which　should　always　be　taken　by　a　bidder　company　when　trying　to　identify　suitable　target　companies　prior　to　an　M&A.　This　paper　proposes　an　approach　to　two-sided　M&A　fits　based　on　a　cross-efficiency　model　with　contrasting　attitudes.　In　this　approach,　firstly,　feasible　M&A　fits　are　screened　using　a　preference　function　from　an　M&A　fit　matrix,　according　to　the　preferences　of　both　the　bidder　companies　and　target　companies　in　terms　of　efficiency　and　return　to　scale.　Secondly,　two-sided　M&A　fits　are　selected　from　a　feasible　M&A　fit　matrix,　according　to　the　value　of　cross-efficiency　with　contrasting　attitudes.　This　allows　for　the　existence　of　contrasting　attitudes　of　peers　toward　an　M&A　fit,　as　opposed　to　the　aggressive,　benevolent　or　neutral　cross-efficiency　evaluation　which　consists　of　just　one　attitude　(either　aggressive,　benevolent　or　indifferent).　Finally,　an　illustrative　example　is　given　to　explain　the　feasibility　and　validity　of　the　two-sided　M&A　fit　strategy.　©　2016　The　OR　Society.