Two new noncentrosymmetric quaternary sulfides, La2Ga2GeS8 (1) and Eu2Ga2GeS7 (2), have been synthesized by high-temperature solid-state reactions. The structure change on going from 1 to 2 to the known Li2Ga2GeS6 (3) nicely shows that the reduced cation charge-compensation requirement causes a decrease in the number of terminal S atoms per formula, which is a key to determining the connectivity of the GaS4 and GeS4 building units. Powder sample 2 exhibits a strong second-harmonic-generation (SHG) response of about 1.6 times the benchmark AgGaS2 at 2.05 mu m laser radiation, a non type I phase-matchable behavior, and a comparable transparency region. The SHG intensities of these compounds originate from the electronic transitions from S 3p states to La/Eu/Li-S, Ga-S, and Ge-S antibonding states according to Vienna ab initio simulation package studies.