A computer system comprises a generally U-shaped base unit (10) and a generally-rectangular travel unit (12) which mates with the base unit, between the legs (34, 36) of the "U". The portable unit contains a complete computer system, including a flip-up monitor screen (14), a disc drive (20), and a detachable keyboard (24). The mating base unit includes expansion slots (30) for additional memory, peripheral equipment controllers, a CRT controller, etc. Also the base unit includes a controller (112) for one or more additional disc drives (26, 28). The facing sides of the legs of the U-shaped base unit have a step-shaped configuration (42, 44, 46) and the portable unit fits onto the step. The bight portion (38) of the base unit has a front connector (49A) for mating with the portable unit and rear connectors (48, 58A) for connection of additional equipment, such as a printer and modem.