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In the Cronquist system, there is no Aquifoliales order: the Aquifoliaceae are placed within the order Celastrales and the others are in other families.
The still older Cronquist system of 1981, which was not based on molecular data, placed the order in subclass Commelinidae of class Liliopsida and included the families Commelinaceae, Mayacaceae, Rapateaceae and Xyridaceae.
Placement of the genus within a family has previously been considered a difficult problem; it has at various times been placed in Capparaceae, Sapindaceae, Goodeniaceae and, in the Cronquist system, Polygalaceae.
The Cronquist system, of 1981, also recognized such a family and placed it in the order Typhales in the subclass Commelinidae in class Liliopsida in division Magnoliophyta.