Qantas and Virgin jets took off from Adelaide early on Wednesday, while their flights through Melbourne and the capital, Canberra, are due to resume.

Services from Sydney, Newcastle and Hobart will begin in the afternoon.

Many travellers spent the night at airports as flights were disrupted for the second time in just over a week.

Last week, tens of thousands of people were stranded as airlines grounded flights as ash from the Puyehue-Cordon Caulle volcano passed over several Australian cities and New Zealand.

By Friday, all flights were running normally, but the ash cloud circled the Earth for a second time and caused further disruption.