For the first time, conjoined twins Abby and Erin Delaney can sleep in separate beds.

The 10-month-old girls from North Carolina were born connected at the head, an extremely rare condition.

Following months of planning and preparation, the pair underwent a successful 11-hour separation surgery last week at Children's Hospital of Philadelphia in southeastern Pennsylvania, according to the hospital.

"Separating conjoined twins is a very complex surgery followed by a long and complicated recovery, but we are very hopeful for a positive outcome," Jesse Taylor, a plastic surgeon who co-led the operation with neurosurgeon Gregory Heuer, said Tuesday in a statement from the hospital.

"Erin and Abby are now recovering in our Paediatric Intensive Care Unit under close monitoring by our expert teams."

With identical twins, an embryo splits in two early in a pregnancy; but with conjoined twins, the embryo does not separate all the way and the twins remain connected, according to the University of Maryland Medical Center.

Conjoined twins are uncommon, occurring once in about every 200,000 births - and craniopagus twins, those who are connected at the head, are the rarest form, accounting for about 2 percent of conjoined twins, according to the medical centre.

The severity of the condition depends on how and where the conjoined twins are connected. One expert said that most craniopagus twins do not survive.

Abby and Erin's parents, Riley and Heather Delaney, learned that their girls were conjoined early last year when Heather Delaney was about 11 weeks pregnant.

Although it was too soon to know whether the twins would be able to be separated, Heather Delaney started traveling from North Carolina to Pennsylvania for her prenatal care.

Eventually, she moved into a hospital facility in Philadelphia for mothers carrying babies with complex congenital conditions, according to the hospital.

On July 24, 2016, Abby and Erin were delivered by C-section 10 weeks prematurely, each weighing about 2 pounds, the hospital said in a statement.

Doctors there worked on a comprehensive plan to try to separate them.

Alan R. Cohen, chief of paediatric neurosurgery at Johns Hopkins Hospital, said that he could not comment on the Delaneys' case specifically but that separating craniopagus twins "can be a high-risk surgery."

Cohen said surgeries are done at major medical centres where teams of neurosurgeons, plastic surgeons, anesthesiologists and critical-care physicians spend months studying patients' brain scans and, often, 3-D models "to try to find the safest way to make the disconnection."

"Depending on where the heads are joined and how much they are fused, that determines the complexity of the operation," Cohen said.

He added that "the most feared complication of the surgery is how to manage the shared blood vessels - particularly the veins that drain the brain - because usually one twin gets the good veins and the other doesn't."

There are also ethical considerations with separation surgery, Cohen said. He said that the twins may not survive the intervention, or sometimes one twin survives and the other does not or is in poor neurological condition.

He said "success" means the surgeons are able to separate the twins, but "in terms of the long-term prognosis, it's usually a long road ahead for the family and the medical team caring for them."

The night before the Delaneys' surgery on June 6, someone posted on a Facebook page set up for the twins.

"The girls have a big procedure tomorrow," the post read. "We ask for as many prayers as you can spare. It will be a long day for us."

For days after, the messages asked others to "bear with us" and "keep praying for us."

Children's Hospital of Philadelphia said about 30 doctors, nurses and other medical personnel worked to separate the twins - a first for the hospital.

The hospital said it has separated 22 other pairs of conjoined twins over the past 60 years but never a pair of craniopagus twins.

The surgery was meticulously orchestrated: Surgical equipment was colour-coded with green and purple tape — one colour assigned to each patient. The medical team worked essentially on one body — and then once the girls were separated — the team split to care for two.

"During the separation surgery, our team first meticulously separated the infants' shared blood vessels and dura, the tough protective membrane surrounding both brains, then moved on to separate the sagittal sinus, the most difficult portion of the operation," Heuer, the neurosurgeon, said in the statement.

"Finally, we divided our team into two halves, one for each of the girls, and finished the reconstruction portion of the surgery."

The hospital said the twins will likely have additional surgeries but plans to send them home later this year.

"When we go home, it's going to be a big party," Heather Delaney said in a statement from the hospital. "Welcome home, baby shower, first birthday."

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