Large coverage lexical resources that bear deep linguistic information have always been considered useful for many natural language processing (NLP) applications including Machine Translation (MT). In this respect, Frame-based resources have been developed for many languages following Frame Semantics and the Berkeley FrameNet project. However, to a great extent, all those efforts have been kept fragmented. Consequentially, the Global FrameNet initiative has been conceived of as a joint effort to bring together FrameNets in different languages. The proposed paper is aimed at describing ongoing work towards developing the Greek (EL) counterpart of the Global FrameNet and our efforts to contribute to the Shared Annotation Task. In the paper, we will elaborate on the annotation methodology employed, the current status and progress made so far, as well as the problems raised during annotation.