A cladistic analysis, primarily based on morphology, is presented from 40 diploid taxa representing the 24 monogenomic genera of the Triticeae. General problems related to the treatment of hybrids and supposedly allopolyploid heterogenomic taxa are highlighted. Special emphasis is given to taxa not traditionally included in Aegilops s.J. Most of the 33 characters used in the analysis are coded as binary. The only four multistate characters in the matrix are treated as unordered. Three diploid species of Bromus are used as outgroup. The number of equally parsimonious trees found is very large (approx. 170000; length = 107, ci = 0.36, ri = 0.75) and the strict consensus tree has an expectedly low level of resolution. However, most of the equally parsimonious trees owe their existence to an unresolved Aegilops clade. If this clade is replaced by its hypothetical ancestor, the number of equally parsimonious trees drops dramatically (48; length = 78, ci = 0.45, ri = 0.76). When trees for which more highly resolved compatible trees exist are excluded, only two trees remain. Bremer support is used as a measure of branch support. The trees based on morphology and on molecular data are largely incongruent.