To date the Erbium Doped Fiber Amplifiers (EDFAs) which have been used in lightwave communications systems can be termed as "lumped" (EDFA) amplifiers. This is because several tens of dBs of gain is obtained in fiber lengths <50 m. It is evident that the signal experiences large excursions in amplitude, which can cause significant interchannel interference in a WDM system. What is needed is a distributed amplification over the whole length of the fiber, so that the gain per unit length just cancels the intrinsic fiber attenuation. This will allow the signal to be maintained at a high level throughout the system, while reducing the Amplified Spontaneous Emission (ASE) and thus resulting in a higher Signal-to-Noise Ratio (SNR) for the system. The first, and a somewhat preliminary, report of such Distributed EDFAs (or DEDFA) was presented recently by a team at AT&T Bell Labs). They showed that fibers can indeed be made with the controlled, very low erbium doping levels, 10-100 parts per billion (ppb) averaged over the core, required for such distributed amplification. Further no significant impurities or other defects are introduced into the fiber, and the environmental added losses, due to radiation, will not impede their use. Due to the importance of the idea of DEDFAs, the theoretical study in this proposal will aim at two part: (i) optimizing the design of the DEDfa and (ii) analyzing its performance in lightwave communication systems, both direct- detection and coherent-detection, so as to determine the ultimate system that can be built, with trade-offs involved.