This contribution constitutes the second phase of the Geosites project of IUGS. This phase started with an open discussion in the greek geoscientific community for the improvement of the geosites framework created during the first phase of the project. The first phase is described in another paper of the present Congress.The criterion for the selection of the geoscientists to send them an information package for this first open discussion was their previous involvement with geological heritage conservation, geotopes protection and management issues. The fruit of the cooperation of the first group, that is, the improved and completed geosites framework together with some geosites as examples of the framework categories, is included in this paper. The format of the framework has changed in this paper (compared with the one of the paper for first phase, of the present congress) in order to make it shorter. The whole framework, categories, geosites-examples, are written in English language as well, because English is the common language of the Geosites programme.The categories refer to both continental and submarine geosites. This product is not closed and static but on the contrary it is open, dynamic and under development. It will obtain gradually and systematically, with the involvement and cooperation of all the more specialists, completeness and a representativity equivalent to the geodiversity of Greece. In this way it will be represented adequately in the European and the world geosites list.