Negotiating teams from the Indonesian government and the rebel Free Aceh Movement have begun a second round of peace talks in Finland.
Gam has previously said it will only accept full independence
The Indonesian government is expected to repeat an offer of special autonomy for Aceh during the three-day talks.
The Aceh rebels have been fighting for independence for the past 30 years.
The first round of talks in Helsinki three weeks ago was considered a big step forward as the parties had not met at all for almost two years.
At this second meeting in Helsinki, they are expected to get down to tackling the details of a future agreement on how to end three decades of bloody conflict in the Aceh region.
Like the last talks, they are being held at the secluded Koeningstedt estate outside Helsinki and are closed to the press.
They are being mediated by former Finnish President and career diplomat Martti Ahtisaari. He is expected to hold a news conference when the talks end on Wednesday.
The Indonesian President, Susilo Bambang Yudhoyono, earlier said the Indonesian government wanted to use the meeting to discuss how its offer of special autonomy for the region could work in practice.
The leadership of the Free Aceh Movement (Gam) said they wanted to see what exactly the Indonesian government had to offer before saying anything about whether they now would be ready to accept autonomy for the region.
Gam has earlier said it will accept nothing short of full independence.
Political analysts in Aceh have said the most important thing for now is that the parties agree on a permanent ceasefire to ensure safety for all involved in the aid operation after the tsunami which devastated the region in December.
A de facto ceasefire has been in place since the disaster but there have been recent reports of continuing clashes between Gam rebels and Indonesian forces.
On Sunday, an Indonesian soldier was killed and seven others were wounded in an ambush by about 30 rebels, Reuters news agency reported.
Nevertheless, there is nothing like the level of violence that existed before the tsunami disaster, and there is an opportunity, however slim, for a more permanent solution to be found, says the BBC Jakarta correspondent Rachel Harvey.
In Aceh's provincial capital, few people seemed to know the talks were even taking place, and care more about surviving with few resources, our correspondent says.
But despite the apparent lack of interest in Banda Aceh, what happens in Helsinki could have a profound impact on Aceh's future prospects.