A system for aspirating fluids from a body by means of negative pressure has: a drainage line for removing the fluid from the body, a fluid collection container connected to the drainage line and used to collect the aspirated fluid, a pump by which the negative pressure used to aspirate the fluid is generated in the drainage line, and an auxiliary line whose end near the body is in fluidic communication with an end, near the body, of the drainage line. In the system, a closed circuit is present or can be generated which interconnects this pump, the auxiliary line, the drainage line and the fluid collection container and through which air or a liquid can be pumped. This system prevents and removes obstructions in the drainage line and also permits a relatively accurate measurement of the negative pressure in the body cavity.