Abstract: In this study, we study the concept of doubly connected geodetic number of a graph. A set SfV in a graph G is a Doubly Connected Geodetic Set [DCGS] if S is a geodetic set and both induced subgraphs < S > and < V-S > are connected. The minimum cardinality of a doubly connected geodetic set and it is denoted by gdc (G) is called doubly connected geodetic number of a graph G. A doubly connected geodetic set of cardinality gdc (G) is called gdc (G)-set. We determine the doubly connected geodetic number in cartesian product, strong product, join of two graphs