We present here Global Index Grammars (GIGs) and the characterizing 2 Stack automaton model (LR-2PDA). We present the techniques to construct an LR parsing table for deterministic Global Index Grammars. GILs include languages which axe beyond the power of Linear Indexed Grammars/Tree Adjoining Grammars. GILs generalize properties of CF Languages in a straightforward way and their descriptive power is relevant at least for natural language and molecular biology phenomena.