Four Hg-based IR nonlinear-optical materials, AHgSnQ(4 )(A = Sr, Ba; Q = S, Se), were discovered and investigated systematically. Their structures are built of two-dimensional [HgSnQ(4)](2-) layers, which are assembled alternately by distorted (HgQ(4) and SnQ(4)) tetrahedra and separated by eight-coordinated A(2+) cations. The two sulfides AHgSnS(4) (A = Ba, Sr) exhibit large second-harmonic-generation (SHG) responses (2.8 and 1.9 x AgGaS2 at 2.09 mu m), as well as large band gaps (2.77 and 2.72 eV). The two selenides AHgSnSe(4) (A = Ba, Sr) show even stronger SHG responses, about 5 times that of AgGaS2. Furthermore, all four compounds show phase-matching behavior, and the results of first-principles calculation elucidate the key role of the HgQ(4) group in the enhanced SHG effect in beta-BaHgSnS4 and BaHgSnSe4.