The recent extreme ultraheavy cosmic-ray observations (Z greater than or equal to 70) are compared with r-process models. A detailed cosmic ray propagation calculation is used to transform the calculated source distributions to those observed at the earth. The r-process production abundances are calculated using different mass formulae and beta-rate formulae; an empirical estimate based on the observed solar-system abundances is also used. There is the continued strong indication of an r-process dominance in the extreme ultraheavy cosmic rays. It is shown that the observed high actinide/Pt ratio in the cosmic rays cannot be fitted with the same r-process calculation which also fits the solar-system material. This result suggests that the cosmic rays probably undergo some preferential acceleration in addition to the apparent general enrichment in heavy (r-process) material. An estimate is also made of the expected relative abundance of superheavy elements in the cosmic rays if the anomalous heavy xenon in carbonaceous chondrites is due to a fissioning superheavy element.