The　purpose　of　this　paper　is　to　develop　a　nonlinear　programming　method　for　solving　a　type　of　cooperative　games　in　which　there　are　multiple　objectives　and　coalitions＇　values　on　objectives　are　expressed　with　intervals,　which　are　called　intervalvalued　multiobjective　cooperative　games　for　short.　In　this　method,　we　define　the　concepts　of　interval-valued　cores　of　interval-valued　multiobjective　cooperative　games　and　satisfactory　degrees　of　comparing　intervals　with　inclusion　and/or　overlap　relations.　The　interval-valued　cores　can　be　computed　by　developing　a　new　two-phase　method　based　on　the　auxiliary　nonlinear　programming　models.　The　proposed　method　can　seek　cooperative　chances　under　the　situations　of　inclusion　and/or　overlap　relations　of　intervals　in　which　the　traditional　interval　ranking　method　may　not　always　assure　that　the　interval-valued　cores　exist.　The　feasibility　and　applicability　of　the　developed　method　are　illustrated　with　a　real　example.　©　2014　IEEE.