Changes of higher-order structure of poly(ethylene glycol) -poly(butadione) (PEG-PBd) di- and triblock copolymers in isothermal crystallization from microphase-separated melts were studied using time-resolved synchrotron small-angle X-ray scattering (SR-SAXS) techniques. Lamellar microphase structure of PEG-PBd with weight fractions fl'EG = 0.57 and 0.51 was destroyed on crystallization and changed to a lamellar structure distinct from that in the melt. A diblock copolymer with f(PEG) = 0.34 crystallized, keeping the cylindrical structure preexisting in the melt. On the other hand, a f(PEG) = 0.7 diblock copolymer whose melt structure was cylindrical showed two kinds of structure changes: at low crystallization temperatures T, the SAXS peak positions changed discontinuously but the structure remained cylindrical, while the structure changed from cylindrical to lamellar at high T,. Triblock copolymers PBd-PEG-PBd with f(PEG) = 0.67 and 0.42 showed a structure change similar to the f(PEG) = 0.57 and 0.51 diblock copolymers. Behavior of structure changes in the melting process was the reverse of that in the crystallization process for all the samples. Crystallization behavior, in particular crystallization kinetics, was also investigated by DSC and polarized optical microscopy (POM.) with a 530 nm retardation plate. Avrami exponents evaluated from DSC results for the block copolymers were almost the same as those for PEG homopolymers even in crystallization from the cylindrical melt, which was quite different from the result in crystallization from a frozen microphase-separated melt reported previously. For the f(PEG) = 0.34 diblock and f(PEG) = 0.42 triblock copolymers with a small-sized microdomain in the melt, overall crystallization rates were suppressed and apparent activation energies were high. No spherulite with a clear Maltese cross was observed by POM, but the crystal region was propagated with irregularly distributed blue- and yellow-colored portions for all the block copolymers including the f(PEG) = 0.34 diblock copolymers. This behavior of the propagation and the above result of Avrami exponents for the f(PEG) = 0.34 copolymer suggest that crystallization can traverse from one cylinder domain to another with preservation of the melt structure. From the kinetic results obtained by both DSC and POM, it was suggested that nucleation was easy for the middle block in the triblock copolymers.