Searches for neutrinoless double beta decays could determine if neutrinos are Majorana particles and could measure their absolute mass scale. The initial stage of the Enriched Xenon Observatory project, EXO-200, will look for two-neutrino and neutrinoless double-beta decays of Xe-136 in a liquid-xenon time-projection chamber. By combining the ionization signal with detection of the scintillation light collected in Large Area Avalanche Photodiodes (LAAPDs), an energy resolution of about 1.4% at the decay energy can be achieved. All construction materials have been systematically selected to minimize naturally-occurring radioactive impurities. An active muon veto is presently under construction. Using these background reduction techniques and the available 200 kg of isotopically enriched xenon (80% in Xe-136), EXO-200 will be soon able to test present constraints on the effective Majorana-neutrino mass. It will also serve to demonstrate the potential performance of a larger-scale EXO experiment which will further reduce backgrounds by detecting the residual Ba ion produced in the decay. Installation of the EXO-200 detector is now in progress at the Waste Isolation Pilot Plant (WIPP) in New Mexico.