We report the structures of three new alkaline earth metal gallium nitrides synthesized as crystals from the elements in sealed Nb tubes at 760 degrees C using Na/Sr and Na/Ca melts as growth media. The materials are all transparent insulators. Yellow Sr3Ga2N4 is isostructural With the previously reported Ba3Ga2N4 and Sr3Al2N4. It crystallizes in Pnna (No. 52) with a = 5.9552(6) Angstrom, b = 10.2753(8) Angstrom, c = 9.5595(9) Angstrom, and Z = 4. It contains infinite chains, (1)(infinity)[GaN4/23-], of trans-edge-shared tetrahedra extending along the b axis. Colorless Ca3Ga2N4 is isostructural with Ca3Al2As4 and gamma-Ca3Al2N4. It crystallizes in C2/c (no. 15) with a = 10.6901(11) Angstrom, b = 8.3655(7) Angstrom, c = 5.5701(4) Angstrom, beta = 91.194(6)degrees, and Z = 4. It contains infinite sheets, (2)(infinity)[GaN4/23-], Of edge- and corner-sharing tetrahedra in the be plane. Orange-yellow Sr3Ga3N5 has a new structure; it crystallizes in P (1) over bar (No. 2) with a = 5.9358(6) Angstrom, b = 7.2383(8) Angstrom, c = 8.6853(12) Angstrom, alpha = 108.332(10)degrees, beta = 103.783(9)degrees, gamma = 95.326(8)degrees, and Z = 2. It is one of the few materials prepared from Na melts which has an infinite three-dimensional framework structure. It contains a (3)(infinity)[Ga3N56-] framework of edge- and corner-sharing GaN4 tetrahedra.