Different chemical compositions of the AlCuFe and the AlCuFeCr systems have been stud led. The liquid melts have been cast in different mould types where the rate of cooling can be varied. The experimental results showed that for slow solidification rates and in the case of the ternary alloys, binary compounds can only be obtained. However, for higher cooling velocities, binary, ternary and quasicrystalline compounds were obtained. In the quaternary case, higher cooling velocities produce an amorphization tendency in the obtained alloy. But for slow rates of cooling, binary, ternary and quasicrystalline compounds were obtained. High rates of cooling in the ternary alloys produce a microstructure with a high density of star-shaped dendrites. Some of these dendritic formations display apparent ten-fold rotational symmetry.