CO emission has been detected from 75 bright infrared galaxies with CZ = 2 000 – 16 000 km/s. These include the most distant and the most luminous galaxies (Arp 55, IR 1713+63) yet detected in CO. All of these galaxies are rich in molecular gas with Mtotal (H2) = 2 × 109 −6x1010 M⊙, and they have a strong far-infrared excess, with LFIR/LB = 2-40 and LFIR (40-400μ) = 1010 – 3 × 1012 L⊙. The primary luminosity source appears to be star formation in molecular clouds. A strong correlation is found between the FIR and 21-cm continuum flux, implying that the IMF is independent of the star formation rate. The ratio LFIR/M(H2) provides a measure of the current rate of star-formation, which is found to be a factor 3-20 larger in these galaxies than for the ensemble of molecular clouds in the Milky Way. VLA maps plus a few high resolution (14″-30″) CO (1-0) and CO (2-1) maps suggest that most of the luminosity comes from core regions 1-3 kpc in size. The abnormal concentration of molecular gas in these galactic cores is presumably the result of a collision or strong interaction with a nearby companion.