 Pastoral settlement followed soon after , with grazing runs established along the Murray and Murrumbidgee as far west as Hay by 1839 . At the time , the area was known as the Murrumbidgee District . Moulamein , in the western Riverina , appears to make legitimate claims as the oldest town in the Riverina , and indeed to being older than Melbourne . The settlers often came into conflict with the indigenous inhabitants . In the Narrandera district , a battle took place between settlers and the local Narrungderra clan at a location now known as Massacre Island , reportedly leaving only one survivor . 
