Explorations of new second harmonic generation materials in Ag + -Hg 2+ /Bi 3+ -selenites systems afforded three new silver selenium oxides, namely, Ag 4 Hg(SeO 3 ) 2 (SeO 4 ) (1), Ag 2 Bi 2 (SeO 3 ) 3 (SeO 4 ) (2) and Ag 5 Bi(SeO 3 ) 4 (3). They exhibit flexible crystal chemistry. Compounds 1 and 2 are mixed valence selenium oxides containing Se(IV) and Se(VI) cations simultaneously. Compounds 1 and 3 exhibit a 3D open framework with 4-, 6-and 8-member polyhedral ring tunnels along a, b and c axes. Compound 1 crystallized in a polar space group and could display a subtle frequency doubling efficiency about 35% of the commercial KH 2 PO 4 (KDP). UV-vis-NIR spectra reveal that compounds 1-3 are wide-band semiconductors with the optical bandgaps of 3.11, 3.65, 3.58 eV respectively. Theoretical calculations disclose that compounds 2 and 3 are indirect band gap structures and their bandgaps are determined by Ag, Bi, Se and O atoms together.