A method and device for managing downloading of a digital content available by progressive downloading onto a content server in a communication network. The content server is accessible via a service gateway of a local network including first and second terminals. The method includes: receiving a request for progressive downloading of first digital content from the first terminal; receiving a request for progressive downloading of second digital content from the second terminal; obtaining rights relating to the terminals on the downloading device including data regarding priority of the first and second terminals, data relating to a priority of use of the downloading device; comparing the data regarding priority of the first terminal with the data regarding priority of the second terminal, so as to define the terminal having priority; downloading the digital content requested by the terminal having priority.