Besides the six established decagonal states of the Al-Co-Ni quasicrystal two more modifications have been discovered by means of transmission electron microscopy. One is a pentagonal quasicrystal with a superstructure found in specimens with a very high Co-content and quenched from the highest possible temperature lying within the stability field of decagonal Al-Co-Ni. Its electron diffraction patterns are characterized by a 5-fold rotation axis as a unique symmetry element as well as superstructure reflections similar to those of a related decagonal phase. The other is a one-dimensional quasicrystal closely related to decagonal Al-Co-Ni. The modulation length of 61 Å along the periodic direction in its pseudo 10-fold diffraction patterns can be assumed to be caused by a strong linear, uniform, phason strain in the material.