This invention relates to a method and apparatus for controlling overload in a data network. The exemplary embodiment is a Broadband Integrated Services Digital Network (B-ISDN) in which data is transmitted within data cells included in a larger data frame using the Asynchronous Transfer Mode (ATM) protocol. In response to the network detecting overload, the network sends slow down messages to selected virtual channels to decrease their data rates. The network also acts to block or decrease resource allocations to transmission requests that are likely to overload the network.