A vacuum-assisted liner system for the socket of a limb prosthesis secures the prosthesis to a residual body portion. A vacuum is created directly between the residual body portion and the socket (8) to hold them together and minimize relative movement between them. The system includes a flexible liner (4) made of an impermeable material, at least a distal part (4D) of the liner being porous to allow the transport of air and fluid directly away from the residual body portion to the outer surface of the liner. A fabric distribution layer (6) is located over the liner (4) and between the liner and the socket (8) to allow transmission of such extracted air and fluid laterally over the liner to an evacuation port (10) in the socket. Also disclosed is a limb apparatus suspension device incorporating the liner system, and a vacuum suspension device which secures a component such as a stamp socket to a residual body portion by creating an evacuated space sealed by intimate contact directly between the socket (8) and a boundary region of the liner (4).