MELBOURNE - Australian doctors admitted high-risk surgery to separate Bangladeshi twins who are joined at the head was "very fiddly" as the operation ballooned past 24 hours on Tuesday.

Two-year-olds Trishna and Krishna remained connected as the team of specialists worked through the night, way past the scheduled finish, to divide their brains and blood vessels.

"It's very fiddly, we have to be meticulous," doctor Ian McKenzie told reporters outside Melbourne's Royal Children's Hospital.

McKenzie said surgeons were battling to avoid neurological damage before finally separating the girls, who were brought to Australia from a Dhaka orphanage two years ago.

Plastic surgeons will then close their skulls with bone and skin tissue to prevent infection, ending one of the most complex procedures in Australian medical history.

The team of 16 specialists worked in shifts through the night, taking regular food and rest breaks and even listening to "light pop" in the operating theatre to stay alert.

Despite the delay, McKenzie said the operation was progressing well although he acknowledged life-threatening risks remained. Doctors give just a one in four chance of both girls surviving.

"The bones are now disconnected ... and a whole lot of things we were worried about are getting better and better as we go," McKenzie said.

"But on the other hand, it's not over yet ... and there are still some life-threatening things happening."

The Children First Foundation flew the girls to Australia because of poor survival rates in their native Bangladesh, where only two children have survived four separation operations in recent years.

Both girls were close to death when they arrived but they were nursed back to health and have undergone a series of preparatory operations.

Separating conjoined twins is a notoriously difficult procedure, with attempts in Britain and Bangladesh both failing over the past year, although Saudi doctors successfully divided a pair of Egyptian brothers in February.

In one of the best known cases, Singapore doctors in 2003 made a vain attempt to separate adult twins - Iranian law graduates Laleh and Ladan Bijani, 29 - who died from severe blood loss after 52 hours of surgery.