Laves phases form the largest group of intermetallic phases. Although they are well known since long, there are still unsolved problems concerning the stability of the respective crystal structures. The Laves phases crystallize with a cubic MgCu2- or a hexagonal MgZn2 -o r MgNi2-type structure which differ only by the particular stacking of the same four-layered structural units. It is still not possible to predict which of the structure types is the stable one for a Laves phase compound AB2. Phase transformations from a cubic low-temperature structure to a hexagonal high-temperature structure were observed as well as stress-induced transformations from the hexagonal structure to the cubic one. In addition, deviations from the stoichiometric composition were reported to result in a change of the stable polytype in various systems. In this first of two consecutive papers dealing with fundamental aspects of the stability of Laves phases, some factors which are known to affect the occurrence and structure type of Laves phases are discussed and it is shown that, at least up to now, the existing models and calculations are not well suited to give a general description of the stability of Laves phases. q 2004 Published by Elsevier Ltd.