Two new neodymium molecular magnets of formula {[Nd(α-fur)3(H2O)2]·DMF}n (1) and {[Nd0.065La0.935(α-fur)3(H2O)2]}n (2), α-fur = C4H3OCOO, have been synthesized. In (1) the furoate ligands, in bidentate bridging mode, consolidate zig-zag chains running along the a-direction. Compound (2) is a magnetically diluted complex of a polymeric chain along the b-axis. Heat capacity, dc magnetization and ac susceptibility measurements have been performed from 1.8 K up to room temperature. Ab initio calculations yielded the gyromagnetic factors gx* = 0.52, gy* = 1.03, gz* = 4.41 for (1) and gx* = 1.35, gy* = 1.98, gz* = 3.88 for (2), and predicted energy gaps of Δ/kB = 125.5 K (1) and Δ/kB = 58.8 K (2). Heat capacity and magnetometry measurements agree with these predictions, and confirm the non-negligible transversal anisotropy of the Kramers doublet ground state. A weak intrachain antiferromagnetic interaction J′/kB = −3.15 × 10−3 K was found for (1). No slow relaxation is observed at H = 0, attributed to the sizable transverse anisotropy component, and/or dipolar or exchange interactions enhancing the quantum tunnelling probability. Under an external applied field as small as 80 Oe, two slow relaxation processes appear: above 3 K the first relaxation mechanism is associated to a combination of Orbach process, with a sizeable activation energy U/kB = 121 K at 1.2 kOe for (1), Raman and direct processes; the second, slowest relaxation mechanism is associated to a direct process, affected by phonon-bottleneck effect. For complex (2) a smaller U/kB = 61 K at 1.2 kOe is found, together with larger g*-transversal terms, and the low-frequency process is quenched. The reported complexes represent rare polymeric Nd single-ion magnets exhibiting high activation energies among the scarce Nd(III) family.