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 0.25Hex-->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.