We present an axiomatisation for weak functional dependencies, i.e disjuctions of functional dependencier, in the presence of several constructions fo rcomplex valuae. Those construction are to the tuple constructor. The theory is smooth and rather uniform, if the union constructor is absent. Its presence, however , complirates all results and proofa significantly. The reason for this is that the union constructors is absent, a subset ot the rules is complete for the in the union constructors is present