Bulk samples of Goalpara, Haver¿, Novo Urei, and carbon-rich veins from all seven ureilites have been analyzed for He, Ne Ar, Kr, and Xe by mass spectrometry by employing the stepwise heating technique. In all cases, trapped rare gases of the fractionated 'planetary' type are found to be strongly enriched in the vein material, up to at least 600-fold over the silicates. Gas contents fo the vein material from different ureilites vary considerably; the range in concentrations increases from a factor of 7 He and Ne to a factor of 70 for Xe. Consequently, the elemental abundance ratios vary as well: 23?4He/132Xe?500; 0.35?20Ne/132Xe?10; 119?36Ar/132Xe?1090, and 0.91?84Kr/132Xe?3.05. The isotopic compositions, on the other hand, are indistinguishable from one another in all cases except for 40Ar.36Ar. Some characteristic ratios are 20Ne22Ne=10.70¿0.25 (for 0.03?21Ne/22Ne?0.05). 36Ar/38Ar=5.26¿0.06, and 129Xe/132Xe=1.035¿0.005. The lowest measured 40Ar/36Ar ratio is (1.17¿0.20) ¿103, which, after correction for the extraction blank, yields a new upper limit for the primordial 40Ar/36Ar ratio of (2.¿1.7) ¿104. Of the main constituents of carbon-rich veins--graphite, diamonds, and kamacite--graphite is shown to be void of trapped gases, while samples which show only the X ray diffraction lines of diamond have very high gas contents. In addition, there must be present at least one more carrier containing noble gases with a nuclide abundance pattern distinctly different from that observed for the diamonds and with gas contents even higher than in the diamonds. Its identity is not known at present. Physical adsorption and ambipolar diffusion are discussed as potential mechanisms responsible for the fractionation pattern observed. For adsorption to make the observed abundances compatible with the predicted ones, heavy neon losses (?99%) must have occurred. If they were accompanied by an isotopic fractionation, it is possible that the neon initially was of solar composition. Ambipolar diffusion predicts the abundance ratios observed for (T?8500 K) provided that a means can be found to incorporate the ions into the carrier without any significant additional fractionation. In this case the isotope ratios observed would correspond to the ones in the partially ionized medium where the incorporation occurred.