The　first　examples　of　silver　fluorotellurites,　namely,　AgTeO2F　and　Ag-2(TeO2F2),　and　the　first　silver　fluoride　tellurite,　Ag3F3(TeF6)(TeO2)(12),　have　been　obtained　successfully　under　mild　hydrothermal　conditions.　AgTeO2F　displays　a　new　2D　structure　composed　of　a　2D　silver　oxide　layer　strengthened　by　1D　[TeO2F](infinity)　chains.　Ag-2(TeO2F2)　exhibits　a　new　3D　construction　consisting　of　a　3D　silver　oxyfluoride　framework　with　1D　polyhedral　ring　channels　occupied　by　the　isolated　TeO2F2　groups.　Ag3F3(TeF6)(TeO2)(12)　features　the　first　3D　neutral　[TeO2](infinity)　open　framework　with　8-　and　4-MPR　channels　along　the　a-,　b-　and　c-axes.　AgTeO2F　and　Ag-2(TeO2F2)　crystallize　in　the　centrosymmetric　space　group　while　Ag3F3(TeF6)(TeO2)(12)　is　in　a　non-centrosymmetric　space　group.　Ag3F3(TeF6)(TeO2)(12)　shows　a　unique　nonlinear　optical　property　with　an　SHG　intensity　of　about　70%　that　of　commercial　KH2PO4,　while　AgTeO2F　and　Ag-2(TeO2F2)　present　an　apparent　linear　optical　property　and　their　birefringence　is　calculated　as　0.078　and　0.032@1064　nm,　respectively.　This　work　further　confirms　that　fluorination　in　tellurium(iv)　oxides　can　greatly　enrich　the　structural　chemistry　and　optical　properties　of　metal　tellurites.