Abstract: ''1201'' Tl-based substituted cuprates of the type (Tl1-xMx) Sr2CuO5 have been synthesized for M = Nb, Ta, or W. These materials do not superconduct due to a statistical distribution of some of the M for Cu. The remarkable feature of these materials is the ordering observed between Tl and M in the (Tl1-xMx-epsilon)O plane. The type of ordering depends on the composition and shows remarkable similarities with the ordering in Ni-Mo or other so-called 1 1/2 0 type fcc-based alloys or with the ordering in rocksalt oxides TiOx. The short-range order, for M = W, can be readily interpreted in terms of a mixing of nano-clusters with two different compositions. These observations of two-dimensional ordering confirm recent ideas about ordering in three-dimensional fcc-based alloys.