The novel multidentate chelating ligands N′-(2-pyridylmethylidene)-2-(2-pyridylmethylideneamino)benzohydrazide (Hpphz) and N′-(2-salicylmethylidene)-2-(2-salicylmethylideneamino)benzohydrazide (H₃sshz), which incorporate both amine and acylhydrazine Schiff base groups, were synthesized and investigated in Dy^III coordination chemistry. The reactions of Hpphz and Dy(OAc)₃·4H₂O have yielded two {Dy₂} featuring double OAc⁻ bridges: [Dy₂(H₂aphz)₂(OAc)₄(ROH)₂] [R = Me (1) and Et (2)], where the Hpphz ligands were in situ hydrolyzed into 2-amino-(2-pyridylmethylideneamino)benzohydrazide ions (H₂aphz⁻). Besides, the reaction between H₃sshz and Dy(NO)₃·6H₂O afforded a [Dy₆(sshz)₄(μ₃-OH)₄(μ₄-O)(MeOH)₄]₂·17.5MeOH·2H₂O cluster (3). This cluster contained two discrete {Dy₆} cores, each of which consisted of a pair of {Dy₃} triangular units. All the complexes displayed a single relaxation process of single-molecule magnet (SMM) behaviors under a zero dc field. Both 1 and 2 showed field-induced dual magnetic-relaxation behaviors. However, their diluted samples (1@Y and 2@Y) only showed one-step relaxation behaviors whether under a zero or applied dc field, indicating that the dual magnetic-relaxation behaviors of 1 and 2 were absent after the dilution. Combined with ab initio calculations, it could be infered that the dual magnetic-relaxation behaviors of 1 and 2 might be ascribled to the joint contributions of the single ion anisotropy and magnetic interactions. Examples of this type are rather rare in previous studies. Ab initio calculations also suggested that the discrepancy between the relaxation processes of 1 and 2 may be caused by the small difference between their magnetic interactions.