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An evolutionary connection between ultraluminous infrared galaxies and quasars is deduced from the observations \nof all 10 infrared galaxies with luminosities L(8-1000 μm) ≥ 10^(12) L⊙, taken from a flux-limited sample of infrared bright galaxies. Images of the infrared galaxies show that nearly all are strongly interacting merger systems with exceptionally luminous nuclei. Millimeter-wave CO observations show that these objects typically contain 0.5-2 x 10^(10) M⊙ of H_2. Optical spectra indicate a mixture of starburst and active galactic nucleus (AGN) energy sources, both of which are apparently fueled by the tremendous reservoir of molecular gas. It is proposed that these ultraluminous infrared galaxies represent the initial, dust-enshrouded stages of quasars. Once these nuclei shed their obscuring dust, allowing the AGN to visually dominate the decaying starburst, they become optically selected quasars. The origin of quasars through the merger of molecular gas-rich spiral galaxies can account for both the increased number of high-luminosity quasars at large redshift, when the universe was smaller and gas supplies less depleted, and the observed "redshift-cutoff" of quasars which represents the epoch after galaxy formation when the first collisions occur. \n