In one embodiment, the present invention includes a multicore processor with first and second groups of cores. The second group can be of a different instruction set architecture (ISA) than the first group or of the same ISA set but having different power and performance support level, and is transparent to an operating system (OS). The processor further includes a migration unit that handles migration requests for a number of different scenarios and causes a context switch to dynamically migrate a process from the second core to a first core of the first group. This dynamic hardware-based context switch can be transparent to the OS. Other embodiments are described and claimed.