Pacing communications between a message sending computer and a message receiving computer that are both members of a message group of a sysplex includes receiving, by the message receiving computer, a message comprising data sent by the message sending computer; determining, by the message receiving computer, to stop receiving a subsequent message from the message sending computer; and transmitting, by the message receiving computer to the message sending computer, a first control message instructing the message sending computer to not send any more messages. Pacing further includes determining, by the message receiving computer, to resume receiving the subsequent message from the message sending computer; and transmitting, by the message receiving computer to the message sending computer, a second control message instructing the message sending computer to resume sending messages.