Crystallization of the new biodegradable polyester poly(butylene azelate) (PBAz) under isothermal and non-isothermal conditions was studied and compared to that of the two homologues, poly(ethylene azelate) (PEAz) and poly(propylene azelate) (PPAz). Among them, poly(butylene azelate) has the faster and easier crystallization, as it was proved by the low supercoolings and lower activation energy needed for nonisothermal crystallization. The enthalpy of melting of the pure crystalline PBAz and the equilibrium melting point were found 36.3 kJ/mol and 67.5 °C, respectively, compared to 34.2 kJ/mol and 62 °C for PEAz and 31.9 kJ/mol and 72.2 for PPAz. The secondary nucleation theory was applied and crystallization regime transitions I/II and II/III were observed at 30 and 39 °C, respectively. Chemical hydrolysis at 30 °C shows very slow rates. On the other hand the enzymatic degradation rates of PBAz were comparable to those of poly(ɛ-caprolactone) (PCL) or PEAz. However, PPAz has much faster enzymatic hydrolysis.