Abstract: Connection control apparatus is provided for use in an ATM network to control ABR connections provided by the network, each such ABR connection having an agreed minimum transmission rate which it is permitted to exceed when there is spare capacity in the network. The apparatus includes: congestion detection circuitry (32, 33) for determining the end-to-end delay experienced by ATM cells of each ABR connection as they pass through the network; and a rate control circuit (30) connected to the said congestion detection circuitry for detecting, based on the determined end-to-end delay, when one of the ABR channels is congested. When congestion in one of the ABR channels is detected the rate control circuit imposes on the ABR connection concerned a maximum transmission rate that is higher than and dependent upon the said agreed minimum transmission rate for the connection concerned.