The Innamincka Dome and associated low-gradient fan in the Strzelecki Desert is the product of Cenozoic crustal warping that has aided formation of an extensive array of palaeochannels, source-bordering transverse dunes and superimposed linear dunes. These dunes have impeded the course of Cooper Creek and provided a repository of evidence for Quaternary climate change as well as the interactive processes between transverse and linear dune formation. At Turra, Gidgealpa and sites nearby are extensive fluvial and aeolian sand bodies that date from marine isotope stages (MIS) 8-3 and the Last Glacial Maximum (LGM) and are now surrounded or buried by overbank mud. The sandy alluvium was deposited on the downstream slope of the dome by large channels transporting abundant bedload, subsequently blown northward to form transverse dunes from what were probably seasonally-exposed bars in a palaeo-Cooper system. Thermoluminescence (TL) and optically stimulated luminescence (OSL) ages demonstrate that the base of the dune complex is at least MIS 7 in age (∼250 ka) but that it has been subsequently reworked by wind with additional sand blown from the river. Source-bordering dunes formed during a period of enhanced river flow and sand supply from ∼120 to 100 ka, with another short episode of the same at ∼85-80 ka and from ∼68 to 53. The LGM was associated with enhanced flows and the supply of dune sediment, from 28 to 18 ka. Pronounced river flow and dune activity occurred in the early to mid Holocene, but there is no evidence of dunes being supplied from Cooper Creek since the LGM. The dunes forming the oldest basal sand units appear to be largely transverse in form and are aligned roughly parallel to adjacent east-west trending palaeochannels. Linear dunes have formed from and over these, and yield basal ages ranging from MIS 5 or MIS 4 but continuing to accrete and rework through to the Holocene. The study results in one of the few detailed chronological investigations of the interaction between transverse and linear dunes. It is apparent that long-distance sand transport has played no significant role in dune formation here for the linear dunes show no significant downwind decline in ages. Linear dunes appear to have accreted vertically from underlying transverse dunes. A wind-rift vertical accretion model with only minor lengthwise extension is the dominant mode of linear dune formation in this section of the Strzelecki Desert, the bulk of dune sediment being sourced from adjacent swales since the LGM.