Cytological observations on eleven species of Ophioglossum revealed low gametic (n) chromosome numbers of 30, 34 and 60 in populations of O.eliminatum, contrasting with an earlier report of n= 90 in the same species. The rest of the species is based on n=120.Cytologically studied species of Ophioglossum exhibit a range of chromosome numbers from n = 30 in O.eliminatum to n=720 in O.reticulatum. The weighted highest common factor (HGF) from all the reported chromosome numbers in twelve species was found to be 30. This number is proposed as the palaeobasic chromosome number for the genuS. Reported chromosome numbers which are not multiples of 30 were subjected to sequential analysis, yielding three distinct ultimate base numbers, 4, 5 and 6, which can produce n= 30 in seven different ways. The neobasic number, n= 120, appears to have arisen through various combinations and permutations of these, theoretically 2401 routes; only a relatively few of these routes exist today, suggesting that extreme selection has been exerted against the majority, and further suggesting that Ophioglossum represents an evolutionary dead end through repeated cycles of polyploidy and is possibly at the verge of extinction. The stoichiometric model of evolution, which derives the various chromosome numbers possessed by the twelve species from the basic and ultimate basic chromosome numbers, is used to explain chromosomal evolution in the genus.