Graph　coloring　has　interesting　real　life　applications　in　optimization　and　network　design.　In　this　paper　some　new　results　on　the　acyclic-edge　coloring,　f-edge　coloring,　g-edge　cover　coloring,　(g,　f)-coloring　and　equitable　edge-coloring　of　graphs　are　introduced.　In　particular,　some　new　results　related　to　the　above　colorings　obtained　by　the　authors　are　given.　Some　new　problems　and　conjectures　are　presented.