The goal of this paper is to present the work carried out up to now for the development of the Greek Text-To-Speech (GRTTS) system by NTUA. The system under consideration is based on the method of concatenative synthesis and follows the Bell Labs approach to this technique. In order that the input text to the GRTTS is translated into continuous synthetic speech the following modules have already been studied and implemented: (i) module for the linguistic analysis of the input text; (ii) the acoustic inventory module. On the same time it is under development the duration module of the GRTTS, for the computation of the appropriate temporal structure of synthesized speech. The objectives of the above studies, in combination with the concatenative synthesis technique, which is one of the simplest methods for speech synthesis, are to bypass most of the problems encountered by other synthesis methods such as articulatory and formant synthesis systems. The major objective is to minimize abrupt discontinuities and thus maximize the naturalness of the synthesized utterances.