The RENiZn (RE = La, Tb), RE2Ni2Zn (RE = La, Ce, Tb) and La3Ni3Zn ternary compounds were synthesized by two methods: by heating in a resistance furnace evacuated quartz ampoules containing Al2O3-crucibles with element pieces and by induction melting in sealed Ta crucibles with subsequent annealing at 400 degrees C. Scanning electron microscopy (SEM) coupled with energy dispersive X-ray spectroscopy (EDXS) was used for examining microstructure and phase composition of some of the alloys. The crystal structures for all the investigated phases were solved or confirmed on single crystal data by applying the direct methods refined by a standard least square procedure: LaNiZn - str. type ZrNiAl, hexagonal, P62m, hP9, a = 0.7285(1), c = 0.3938(1) nm, wR(2) = 0.0534, 257 F-2 values, 14 variables; a = 0.7044(1), c = 0.3782(1) nm, wR(2) = 0.0447, 236 F-2 values, 14 variables for TbNiZn; La2Ni2Zn - str. type Pr2Ni2Al, orthorhombic, Immm, oI10, a = 0.4381(1), b = 0.5459(1) c = 0.8605(2) nm, wR(2) = 0.0824, 223 F-2 values, 13 variables; a = 0.4365(1), b = 0.5430(1) c = 0.8279(2) nm, wR(2) = 0.0635, 209 F-2 values, 13 variables for Ce2Ni2Zn; a = 0.4209(1), b = 0.5366(1) c = 0.8165 (1) nm, wR(2) = 0.0757, 200 F-2 values, 13 variables for Tb2Ni2Zn; La3Ni3Zn - str. type Y3Co3Ga, orthorhombic, Cmcm, oS28, a = 0.4276(1), b = 1.0310(2) c = 1.3636(3) nm, wR(2) = 0.0859, 579 F-2 values, 26 variables. The structural peculiarities of these compounds and their relations are discussed.