A subset D of vertices of a graph G is called a global neighbourhood dominating set(gnd - set) if D is a dominating set for both G and GN, where GN is the neighbourhood graph of G. The global neighbourhood domination number(gnd - number) is the minimum cardinality of a global neighbourhood dominating set of G and is denoted by γ gn(G). In this paper sharp bounds for γ gn, are supplied for graphs whose girth is greater than three. Exact values ofthis number for paths and cycles are presented as well. The characterization result for a subset ofthe vertex set of G to be a global neighbourhood dominating set for G is given and also characterized the graphs of order n having gnd -numbers 1, 2, n — 1,n — 2, n.