Chromosome cytology of Iridaceae in the New World is reviewed in detail, and original counts for nineteen species are presented, four of these first re- ports for genera. A tribal classification, based in part on cytology but also on mor- phological criteria, is outined in which three major groups are recognized, Sisyrin- chieae, Trimezieae, and Tigridieae, the latter divided into Cipurinae and Tigridiinae. No decision has been made on whether to recognize Sisyrinchioideae as a subfamily distinct from Iridoideae. Sisyrinchieae comprises two karyotype groups Libertia (x = 19) and Orthrosanthus (x = 9) with tiny chromosomes and Sisy- rinchium and Phaiophleps, both probably also x = 9 but with medium-sized chromo- somes. Trimezieae have medium to large chromosomes and are cytologically diverse with n = 13 and 26 in Trimezia and n = 8, 9, and 16 in Neomarica. Tigridieae have x = 7 and bimodal karyotypes of one or two long pairs and five or six much smaller pairs. Tigridiinae appear polyploid, x = 14, with two long and 12 short pairs. The first counts for ten species and four genera presented here bring to 18 the number of Neotropical genera known cytologically, more than half the total, but less than 20% of the species in this area have been counted. Of the approximately 85 genera and 1500 species of the Iridaceae, some 46 genera and about 1000 species occur in Africa south of the Sahara, mainly in southern Africa, making it the major center for Iri- daceae. However, there are in the Neotropics some 30 genera and 250 species of which about 20 genera and almost all species are endemic, making this area the second richest for the family. In contrast with the African species, the systematics and cytology of which are comparatively well understood, Neotropical Iridaceae are poorly known. There are virtually no modern generic revisions, and existing studies, many dating from the late nineteenth century, were based on very little material often of poor quality. Cytology of only some 40 species in 18 genera of the family in this area is known. The present paper is an attempt to bring together available cytological data, to present several new chromosome counts including ten new reports for species (four of which are first reports for their genera), and to draw what systematic conclusions are possible from this information. A classification below family level is out- lined in which three tribes are recognized, in one of these, Tigridieae, two subtribes are proposed. Tribes are not here assigned to subfamily.