In this paper we describe an efficient method for the synthesis of new heterocyclic systems: furo[2,3-c]-2,7-naphthyridines 6, as well as a new method for the preparation of 1,3-diamino-2,7-naphthyridines 11. For the first time, a Smiles rearrangement was carried out in the 2,7-naphthyridine series, thus gaining the opportunity to synthesize 1-amino-3-oxo-2,7-naphthyridines 4, which are the starting compounds for obtaining furo[2,3-c]-2,7-naphthyridines. The cyclization of alkoxyacetamides 9 proceeds via two different processes: the expected formation of furo[2,3-c]-2,7-naphthyridines 10 and the ‘unexpected’ formation of 1,3-diamino-2,7-naphthyridines 11 (via a Smiles type rearrangement).