Two one-dimensional dysprosium(iii) complexes based on α-glycine (gly) and β-alanine (β-ala) amino acids, with the formula {[Dy2(gly)6(H2O)4](ClO4)6·5H2O}n (1) and {[Dy2(β-ala)6(H2O)4](ClO4)6·H2O}n (2), have been synthesised and characterised structurally and magnetically. Both compounds crystallise in the triclinic system with the space group P1[combining macron]. In 1, two DyIII ions are eight-coordinate and bound to six oxygen atoms from six gly ligands and two oxygen atoms from two water molecules, showing different geometries (bicapped trigonal prism and square antiprism). In 2, two DyIII ions are nine-coordinate and bound to seven oxygen atoms from six β-ala ligands and two oxygen atoms from two water molecules in the same geometry (capped square antiprism). In the crystal packing of both compounds, cationic {[Dy2(L)6(H2O)4]6+}n [L = α-glycine (1) and β-alanine (2)] chains, ClO4- anions, and water molecules generate a network connected through H-bonding interactions. The study of the magnetic properties of 1 and 2 through dc magnetic susceptibility measurements reveals different magnetic behaviour 1 and 2. In addition, ac magnetic susceptibility measurements show a field-induced slow relaxation of magnetisation for both compounds, pointing out that the single-molecule magnet (SMM) phenomenon occurs in both 1 and 2.