For asymmetric diblock copolymers under steady shear flow, the orientational phase transitions in the hexagonal cylinder phase and the kinetics of lamellar to hexagonal phase transition were studied based on the time-dependent Ginzburg-Landau approach. As to orientational phase transitions in the hexagonal cylinder phase, the simulation results show that the parallel orientation is stable at low shear rate and the perpendicular orientation is stable at high shear rate. In addition, different kinetic pathways of lamellar phase to hexagonal phase transition are observed after a sudden temperature jump from one phase to other. When the temperature jump is deep into the hexagonal phase from the shear-orientated lamellar phase under steady shear flow, the lamellae are transformed into hexagonally ordered cylinders directly via the short so-called modulated instability of the lamellar layers. However, if the temperature jump is only slight into the hexagonal phase with or without steady shear flow, lamellae are transformed into hexagonally ordered cylinders going through a distinct modulated and perforated lamellar phase stage. Moreover, without steady shear flow the perforated lamellar phase stage can survive for longer time, indicating that the steady shear flow cannot lead to stabilization of perforated lamellar phase. The simulation results also indicate that the perforated lamellar phase has abab... stacking. (C) 2004 Published by Elsevier Ltd.