The Gamma formalism is a high level parallel programming tool without artificial sequentiality. P. Fradet and D.Le Metayer pr oposed recently a model of structured Gamma which makes it easy for the programm er to structure the data and to specify particular control strategies. It also m akes the automatic analysis of programs easier. Without relying on the “address ” concept used by them, a more general form of the structured Gamma is proposed and its syntax and semantics are described in this paper. Types of structured m ultisets have been discussed at two levels. The author also shows that the new d efinition keeps the theoretic results, such as static type checking of programs untouched.