A subdivision of the stability region of decagonal Al-Co-Ni quasicrystals into eight different structural modifications is presented for the temperature against composition section along the maximum extension of the decagonal phase. The only methods identifying this subdivision are transmission electron microscopy techniques. Besides two decagonal superstructures (one of which also exists as a high-temperature modification), two variants of the basic decagonal state were observed. Also, a one-dimensionally periodic fivefold quasicrystal (together with its high-temperature superstructure modification) and a one-dimensional quasicrystal are parts of the quasicrystalline stability region. Both have a close structural relationship to the decagonal states. All samples investigated were obtained by quenching from the corresponding temperatures. The eight modifications can be differentiated by a set of attributes, especially by their characteristic diffraction patterns taken with the electron beam parallel to the unique periodic axis.