The phase state and the kinetics of the order-to-order transitions have been studied in a series of poly(isoprene-b-ethylene oxide) (PI-PEO) diblock copolymers with a PI volume fraction in the range 0.25<f(PI)<0.92, using small angle x-ray scattering (SAXS), and rheology. The mean-field theory (MFT) structure factor is used to describe the SAXS profiles in the disordered phase and to extract the temperature dependence of the interaction parameter chi(T). In general, an agreement is found with the phase diagram proposed by an extended MFT, except at f(PI) = 0.61 where the following sequence of phases was found: L-c-->Hex-->Gyroid-->Dis (L-c is the crystalline lamellar phase, Hex signifies hexagonally packed cylinders, Gyroid is the bicontinuous cubic network with the Ia (3) over bar d symmetry, and Dis is the disordered phase). We found that crystallization disrupts the amorphous ordered morphologies and imposes a layered structure (L-c). The study of the kinetics of the Hex to L-c and the Hex to Gyroid transitions is facilitated by the different viscoelastic contrast and the distinctly different scattering patterns of the three phases involved (L-c, Hex, Gyroid). Our studies show that it is possible to undercool and overheat ordered phases just as we can undercool the disordered phase. The transformation from the Hex to the L-c phase proceeds via a heterogeneous nucleation and growth process and results in the formation of a spherulitic superstructure composed from stacks of lamellar crystals. The transformation of the Hex to the Gyroid phase involves two steps. The first step-which is too fast to be picked up by rheology-involves fluctuations of the hexagonal phase. The second "slow" step involves a nucleation and growth process of elongated objects. The transformation proceeds nearly epitaxially and has an activation energy of 47 kcal/mol which is typical for a collective process. (C) 1999 American Institute of Physics. [S0021-9606(99)52001-1].