By　applying　the　existence　theorem　of　maximal　elements,　some　new　collectively　fixed-point　theorems　for　a　family　of　set-valued　mappings　defined　on　the　product　space　of　noncompact　FC-space　are　proved　and　some　new　theorems　about　minimax　inequality　involving　two　functions　are　given　to　show　the　relations　of　fixed-point　theorem　and　minimax　inequality　in　FC-spaces.　These　results　improve　and　generalize　many　important　results　in　the　recent　literature.　(c)　2006　Elsevier　Inc.　All　rights　reserved.