An apparatus comprises transaction handling circuitry to issue memory access transactions, each memory access transaction specifying an epoch identifier indicative of a current epoch in which the memory access transaction is issued; transaction tracking circuitry to track, for each of at least two epochs, a number of outstanding memory access transactions issued in that epoch; barrier termination circuitry to signal completion of a barrier termination command when the transaction tracking circuitry indicates that there are no outstanding memory access transactions remaining which were issued in one or more epochs preceding a barrier point; and epoch changing circuitry to change the current epoch to a next epoch, in response to a barrier point signal representing said barrier point. This helps to reduce the circuit area overhead for tracking completion of memory access transactions preceding a barrier point.