Quaternary Zr-Cu-Ni-Al is one of the best glass forming alloys known. In a narrow concentration range icosahedral quasicrystals are formed upon annealing; in Zr69.5Cu12Ni11Al7.5 the metastable primitive icosahedral phase is probably oxygen stabilized. At slightly higher oxygen contents (about 1 at.%) the formation of a metastable fcc "big-cube" phase (NiTi2-type) is competing with very high nucleation rates. The aim of this paper is to investigate in detail the formation of quasicrystals as well as microstructures consisting of the "big-cube" phase in order to design in particular nanocrystalline structures by controlled crystallization. Nucleation rates were measured by means of crystallization statistics. By modeling the obtained nucleation rates in the framework of diffusion controlled classical nucleation interfacial energies as well as melting temperatures for the metastable phases could be derived. Atomic mobility was estimated from growth data. Using these data TTT-diagrams can be drawn and microstructures (for example nanocrystalline) predicted. The phase selection during the formation of the metastable structures was observed to depend strongly not only on the exchange of the Zr by Hf or Ti, but also on the late transition elements chosen, hydrogen or oxygen contamination as well as on alloying with small amounts of other elements for example Si, Sn, Y or Mo. Regarding the influence of the late transition metals there is some evidence that the quasicrystals are a hybrid of two structural elements, i.e. the tetragonal Zr2Ni (Al2Cu) and the tetragonal Zr2Cu (MoSi2) structure. The mentioned alloying elements as well as oxygen and hydrogen are assumed to influence the arrangement of the structural elements towards one or the other structure.