A memory controller with an interface for providing a connection to a plurality of memory devices at least one of said plurality of memory devices supporting burst mode data transfers comprises data interface circuitry for connecting to a plurality of separate data buses for communicating data signals between said memory controller and a respective one of said memory devices, each of said data buses providing a dedicated data signal path to a different one of said memory devices, address interface circuitry for connecting to a common address bus for communicating address signals to each of said memory devices on a shared address signal path, address signals which are directed to different ones of said memory devices being time division multiplexed together on said common address bus, and device selecting circuitry for generating one or more device selecting signals synchronised with said time division multiplexing of said common address bus to select that memory device to which address signals currently asserted on said common address bus are directed. In this way, an increased bandwidth memory controller can be provided which is efficient for both short, narrow and long and wide burst lengths and which has interface circuitry with a relatively low pin count.