Explorations　of　new　second　harmonic　generation　materials　in　Ag+-Hg2+/Bi3+-selenites　systems　afforded　three　new　silver　selenium　oxides,　namely,　Ag4Hg(SeO3)2(SeO4)　(1),　Ag2Bi2(SeO3)3(SeO4)　(2)　and　Ag5Bi(SeO3)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　KH2PO4　(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.　©　2019,　Science　China　Press　and　Springer-Verlag　GmbH　Germany,　part　of　Springer　Nature.