Complete distriburivity is an old theme in lattice theory: the basic results were already proved in the early fifties by G.N. Raney. Some new features of completely distributive lattices have bet.. &scovered recently by P. Dwinger [5] and K.H. Hofmann [9]. The backg ound for [Q] is the categorical equivalence between completely distributive lattices and continuous posers, due to R.-E. Hoffmann (see [2, pp. 159-2081) and J.D. Lawson [12]. It is therefore natural to give a presentation of these matters in a more general framework: the category of Z-continuous posets. The study of Z-continuity was suggested by J.B. Wright et al. (14, p. 761: “... it may be only a curiosity, but we think it would be interesting to investigate this generalized concept . . . ’ ’ . The choice of morphisms is net obvious at least in the non-complete case. Galois connections constitute the main ingredient. For continuous lattices and their generalizations, Galois connections play an important rGle anyway, see [3], 181, [ 1 ‘I] and [ 131. Now, morphisms between Z-continuous posets can be characterized in terms of pairs of adjoint maps. Instances of this adjunction lemma appear in papers by L. Geissinger and W. Graves [6], K.H. Hofmann and J. Lawson [lo], and K.H. Hofmann and A. Stralka [l I]. The present paper focusses on the application of Galois connections to continuous posets and their generalizations. Thus we define Z-morphisms (as certain Galois maps), prove the adjunction lemma and show that Z-morphisms preserve various kinds of Z-continuity. Then the Z-version of the following fact is readily obtained: a lattice is continuous if and only if it is the image of an algebraic lattice under a Lawson-continuous map. Moreover, the images of Z-continuous posets under Z-morphisms can be characterized intrinsically. This, for instance, applies to the results in [5]. We assume that the reader is familiar with completely distributive lattices (cf. [I] 9 171) and continuous lattices (cf. [73, and [2] for more recent results).