The notion of a positive relation between geographical range and speciation rate or speciation probability may go back to Darwin, but a negative relation between these parameters is equally plausible. Here, we test these alternatives in fossil and living molluscan taxa. Late Cretaceous gastropod genera exhibit a strong negative relation between the geographical ranges of constituent species and speciation rate per species per million years; this result is robust to sampling biases against small–bodied taxa and is not attributable to phylogenetic effects. They also exhibit weak inverse or non–significant relations between geographical range and (i) the total number of species produced over the 18 million year timeframe, and (ii) the number of species in a single timeplane. Sister–group comparisons using extant molluscan species also show a non–significant relation between median geographical range and species richness of genera. These results support the view that the factors promoting broad geographical ranges also tend to damp speciation rates. They also demonstrate that a strong inverse relation between per–species speciation rate and geographical range need not be reflected in analyses conducted within a single timeplane, underscoring the inadequacy of treating net speciation as a proxy for raw per–taxon rates.