Studies of solid-state structures under different crystallization conditions, melting behavior, and crystal growth kinetics are reported for biodegradable aliphatic poly(butylene succinate) (PBS) and its random copolyesters of poly(butylene succinate-co-14 mol %ethylene succinate) [P(BS-co-14 mol %ES)] and poly(butylene succinate-co-15 mol %hexamethylene succinate) [P(BS-co-15 mol %HS)]. The crystal structures of two copolyesters determined by wide-angle X-ray diffraction (WAXD) are the same as that of the PBS homopolymer, suggesting that the second comonomers ES or HS units are excluded from the crystalline core and are in an amorphous state. The further investigations on the crystalline and amorphous phase structures and sizes by small-angle X-ray scattering (SAXS) method have provided quantitative evidence that the existence of second comonomers increases the amorphous thickness of copolyesters but that the influences of comonomers on the lamellar crystal structure and size of copolyesters are complicated. The origin of the complexity and its influences on the equilibrium melting temperature T-m(o) of copolyester are discussed in the present paper. Gibbs-Thomson and Hoffman-Weeks equations were applied for the determination of T-m(o) of PBS, P(BS-co-14 mol %ES), and P(BS-co-15 mol %HS)-three samples. Two equations gave different T,1,0 values for each sample. On the basis of the Gibbs-Thomson equation, the P(BS-co-15 mol %HS) copolyester has the same T-m(o) value as that of the PBS homopolymer, while the P(BS-co-14 mol %ES) copolyester has a lower one. This is due to the different influences of the second comonomers on the crystalline phase structure indicated by SAXS results, and the Gibbs-Thomson equation has been suggested to be more reliable. The crystal growth kinetics of the three samples was analyzed by using the secondary nucleation theory, and the influences of various parameters on the regime transition and nucleation constant were studied. Meanwhile some interrelations between regime transition temperature and melting behavior were found for the three samples.