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The R 3TiSb5 ternary compounds, with R a light rare earth (La to Sm) have been reported to crystallize with the anti-Hf5CuSn3-type hexagonal structure (Pearson’s symbol hP18; space-group P63/mcm, N. 193). An early article that reported possible superconductivity in some of these intermetallic phases (namely those with R = La, Ce, and Nd) caught our attention. In this work, we have now refined the crystal structure of the R 3TiSb5 compounds with R = Ce, Pr and Nd by Rietveld methods using high-resolution neutron powder diffraction data. The magnetic ground states of these intermetallics have been investigated by low-temperature magnetization and high-intensity neutron diffraction. We find two different magnetic transitions corresponding to two related magnetic structures at T N1 = 4.8 K (k 1 = [0, 1/2, 1/8]) and T N2 = 3.4 K (k 2 = [0, 0, 1/8]), respectively for Ce3TiSb5. However, the magnetic ordering appears to occur following a peculiar hysteresis: the k 2-type magnetic structure develops only after the k 1-type phase fraction has first slowly ordered with time and the size of the ordered Ce3+ magnetic moment has become large enough to induce the second magnetic transition. At T = 1.5 K the maximum amplitude of the Ce moment in the coexisting phases amounts to μ Ce = 2.15 μ B. For Nd3TiSb5 an antiferromagnetic ordering below T N = 5.2 K into a relatively simpler commensurate magnetic structure with a magnetic moment of μ Nd = 2.14(3) μ B and magnetic propagation vector of k = [0, 0, 0], was determined. No evidence of superconductivity has been found in Nd3TiSb5. Finally, Pr3TiSb5 does not show any ordering down to 1.5 K in neutron diffraction while an antiferromagnetic ground state is detected in magnetization measurements. There is no sign of magnetic contribution from Ti atoms found in any of the studied compounds.