A method for managing streaming of a digital content item within a multimedia content reader terminal, from a communication network. The multimedia content reader terminal is able to be a content source of a rendering terminal. The rendering terminal has a plurality of selectable digital content sources. The method includes the following steps which are executed when the content reader terminal is selected as digital content source, called first source: detecting, during reading of a first content item by the reader terminal, selection of a source, called second source, other than the first source; reading and rendering a second content item originating from the second source instead of the first content item; and the detection step triggering a step of modifying the operation of the reader terminal in connection with the reading of the first content item.