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　interval-valued　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.