The present invention relates to a supply device for a channel (8), in particular within a hollow catheter (1), and to a method for operating a supply device of this type that supplies a channel (8) with a liquid and has two pumps (10, 19) arranged at points of the channel distanced from one another, characterized in that the parameter values of at least one operating parameter of both pumps are coordinated with one another in a controlled manner. As a result of the method, interruption-free and precisely controllable operation is to be ensured with simple structural means, in particular in the case of use of wear-free diaphragm pumps.