This　paper　addresses　continuous　fusion　frames　and　fusion　pairs　which　are　extensions　of　discrete　fusion　frames　and　continuous　frames.　The　study　of　equalities　and　inequalities　for　various　frames　has　seen　great　achievements.　In　this　paper,　using　operator　methods　we　establish　some　new　inequalities　for　continuous　fusion　frames　and　fusion　pairs.　Our　results　extend　and　improve　ones　obtained　by　Balan,　Casazza　and　Gavruta.