Allophylus, at present with c. 255 accepted species, is considered as one of the largest genera of the Sapindaceae. It is distributed throughout the tropics of the Old and the New World, and shows a wide ecological range. Although somewhat variable in vegetative characters, there is a striking homogeneity in fertile characters, by which the generic disposition is easily spotted all over the world. Specific delimitation is renowned difficult in this genus (chapter 2). An analysis of the revision given by Radlkofer in his monograph of the Sapindaceae in ‘Das Pflanzenreich’, Heft 98 (1931—34) reveals that the characters, accepted by him as diagnostic, are all extremely vague, and often grading or overlapping. Of course, the species defined by these characters in most cases appeared to be hardly better (chapter 3). A revision of the genus brought to light that in all three tropical areas the picture is dominated by one central species against which most of the others can not sharply be delimited. Moreover, these three complexes have much in common and appear to be connected by several pairs of mutually hardly separable species. This made it virtually impossible to divide the complex on the specific level (chapter 4). In chapter 5 some theoretical considerations have been given on the possible background of such a widely spread and variable complex. A definite conclusion on this background could not be reached. Phenetically, only one species is accepted, which is named Allophylus cobbe (L.) Raeusch. (chapter 6). It is advised to designate the locally recognizable forms as ‘races’, defined as ‘a population or a group of populations which in a restricted area is morphologically (hence probably genetically), mostly ecologically, and sometimes geographically fully or at least to appreciable degree separable from other such entities’. These races should preferably be named informally by adding in brackets and parentheses either a specific epithet or some ecological, geographic, or morphological designation. In chapter 8 an alphabetical enumeration is given of all the names which either have been accepted by Radlkofer, or were mentioned by him but not evaluated, or were overlooked by him, or published later. With every name critical remarks are made as to possible relationships and, if necessary, nomenclature.