The concept of δ(δg)* - closed set in bitopological spaces (briefly BTS) was introduced in this paper. It specifically looked into and characterized concepts related like δ(δg)*- interior and δ(δg)*- closure of a set, and ????i ????j – closed sets. This paper proves that every ????j – δ-closed set and ????i ????j δg* -closed sets are ????i ????j δ(δg)*-closed. It is also shows that the family of all ????i ????j δ(δg)*-closed (resp. ????i ????j δ(δg)*-open) sets is not equal to ????j ????i δ(δg)*-closed.