The effect of the microphase separation structure in the melt on crystallizability and crystallization kinetics was studied for poly(tetrahydrofuran)-polystyrene diblock copolymers (PTHF-PS) which has a glassy amorphous component. Four binds of copolymers, Block I, Block 2, Block 3 and Block 4 with PTHF compositions of 59, 51, 38 and 29 vol%, respectively, were employed and their crystallization behavior was compared with the PTHF/PS blends as well as the PTHF homopolymers. Crystallization of Block 2, Block 3 and Block 4 was much suppressed, in particular no crystallization was detected for Block 4 even in a long crystallization time and at a high supercooling degree. The blends of Block 4 with the PTHF homopolymer also did not crystallize in the total PTHF content less than about 40%. It was concluded from these results that crystallization from the semidiscontinuous microdomain such as lamellar and cylindrical ones was much suppressed and that crystallization did not occur inside the discontinuous or spherical microdomain surrounded by the glassy matrix. The Avrami exponent was extremely small for Block 2 and Block 3, which suggested that their crystallization occurred under a high spatial constraint. The linear overall rate constant of crystallization for Block 1 was smaller than the blends and homopolymers, but the apparent activation energy of crystallization of Block I was not so different from that of the blends and homopolymers. For Block 2 and Block 3, on the other hand, the rate constant was small and the apparent activation energy was much high. The interfacial free energy of Block 2 and Block 3 estimated using the Lauritzen-Hoffman theory was also large. (C) 2001 Elsevier Science Ltd. All rights reserved.