Abstract: The invention relates to the synthesis of polyoxygenated nitrogen systems, comprising reactions between enamines of 1,3-dioxan-5-ones and nitroolefins. More specifically, the invention relates to the reaction between enamines having formula II which are derived from 1,3-dioxan-5-ones I and nitroolefins having formula III. In this way, novel polyoxygenated nitrogen systems are generated having formula IV and V, which, as they are or following simple transformations, constitute synthetic intermediates and/or analogues of different systems of proven biological/pharmacological interest, such as certain antibiotics, or tetrodotoxin, pancratistatin or the analogues thereof. The aforementioned reactions involve the use of enamines II in Michael-type addition reactions and in direct annealing processes with double acceptor systems at relative positions 1, 3. Said N acceptors include nitroolefins III, wherein R?CHO (alphanitroenals).