To study the influence of hydrazine functions in the ligand skeleton, we designed the heptadentate HYD ligand (2,2',2″,2‴-(2,2'-(pyridine-2,6-diyl)bis(2-methylhydrazine-2,1,1-triyl)) tetraacetic acid) and compared the thermodynamic, kinetic, and relaxation properties of its Ln(3+) complexes to those of the parent pyridine (Py) analogues without hydrazine (Py = 2,6-pyridinebis(methanamine)-N,N,N',N'-tetraacetic acid). The protonation constants of HYD were determined by pH-potentiometric measurements, and assigned by a combination of UV-visible and NMR spectroscopies. The protonation sequence is rather unusual and illustrates that small structural changes can strongly influence ligand basicity. The first protonation step occurs on the pyridine nitrogen in the basic region, followed by two hydrazine nitrogens and the carboxylate groups at acidic pH. Contrary to Py, HYD self-aggregates through a pH-dependent process (from pH ca. 4). Thermodynamic stability constants have been obtained by pH-potentiometry and UV-visible spectrophotometry for various Ln$^{3+}$ and physiological cations (Zn$^{2+}$, Ca$^{2+}$, Cu$^{2+}$). LnHYD stability constants show the same trend as those of LnDTPA complexes along the Ln$^{3+}$ series, with log K = 18.33 for Gd$^{3+}$, comparable to the Py analogue. CuHYD has a particularly high stability (log K > 19) preventing its determination from pH-potentiometric measurements. The stability constant of CuPy was also revisited and found to be underestimated in previous studies, highlighting that UV-visible spectrophotometry is often indispensable to obtain reliable stability constants for Cu$^{2+}$ chelates. The dissociation of GdL, assessed by studying the Cu$^{2+}$-exchange reaction, occurs mainly via an acid-catalyzed process, with limited contribution from direct Cu$^{2+}$ attack. The kinetic inertness of GdHYD is remarkable for a linear bishydrated chelate; the 25-fold increase in the dissociation half-life with respect to the monohydrated commercial contrast agent GdDTPA (t$_{1/2}$ = 5298 h for GdHYD vs 202 h for GdDTPA) is related to the rigidity of the HYD ligand due to the pyridine and methylated hydrazine functions of the backbone. A combined analysis of variable-temperature $^{17}$O NMR and NMRD data on GdHYD yielded the microscopic parameters influencing relaxation properties. The high relaxivity ($r_1$ = 7.7 mM$^{-1}$ s$^{-1}$ at 20 MHz, 25 °C) results from the bishydrated character of the complex combined with an optimized water exchange rate ($k_{ex}^{298}$) = 7.8 × 10$^6$ s$^{-1}$). The two inner-sphere water molecules are not replaced through interaction with biological cations such as carbonate, citrate, and phosphate as monitored by $^1$H relaxivity and luminescence lifetime measurements.