This thesis deals with generalized fibre spaces. It improves upon existing definitions and introduces new ones. It establishes the category of pairs and the category of g.f.s. The relationship between classical fibre spaces and generalized fibre spaces is examined. The induced g.f.s. is defined as well as the concept of section and it is established that the lifting of a fully regular continuous g-function is equivalent to the existence of a section in the induced g.f.s. Finally the lifting theorem for g.f.s. is stated and proved. / Thesis / Doctor of Philosophy (PhD)