The invention relates to a supply device for a channel (8), in particular within a hollow catheter (1), and to a method for operating such a supply device which supplies a liquid to a channel (8), comprising two pumps (10, 19) arranged at mutually spaced locations of the channel. The invention is characterized in that the parameter values of at least one operating parameter of the two pumps are controlled in a coordinated manner. Using the method, a trouble-free operation which can be precisely controlled is to be ensured using simple structural means in particular when using wear-free membrane pumps.