Seven inorganic salts of 3,5-diamino-1,2,4-triazole (dat) with inorganic acids were prepared within our project focused on the crystal engineering of novel NLO materials and their X-ray structures were determined. Three triclinic compounds, dat(1+) selenate dihydrate, dat(1+) sulphate dihydrate and dat(1+) perchlorate, crystallize in the space group P. Three monoclinic structures of dat(1+) – i.e. nitrate, chloride hemihydrate and hydrogen phosphite crystallize in P2₁/c, P2₁/n and P2₁/c, respectively. Finally, the most promising structure of dat(1+) dihydrogen phosphate is orthorhombic (the space group Fdd2). The structure is formed by anionic layers parallel to the ac plane and the cationic chains parallel to the c axis. The FTIR and Raman spectra of the title compounds have been recorded and discussed. The assignment of the spectra is based on a quantum-chemical calculation and the factor group analysis. Quantitative powder measurements of the second harmonic generation of the only non-centrosymmetric dat(1+) dihydrogen phosphate at 1064 nm were performed and a relative efficiency equal to KDP (i.e. potassium dihydrogen phosphate) was observed. The consequent study of single crystal samples enabled the estimation of NLO tensor coefficients of this material.