NEW YORK – Arlene Aguirre must have thought she was dreaming: The mom, whose 2-year-old sons were born joined at the head, awoke to learn that her greatest wish had come true.

“I knelt down and took her hand, and I said, “Arlene, you now have two separate baby boys,”‘ Dr. David Staffenberg recalled Thursday at Montefiore Medical Center in the Bronx – the site of Wednesday night’s medical miracle.

The mother began to weep tears of joy at the news.

She held her hands to her face – overwhelmed by the possibility her sons Carl and Clarence would finally be able to live independently.

“She really was speechless,” said Staffenberg, who spoke to her at 10:35 p.m., two minutes after the boys, conjoined at the tops of their heads, were pulled apart and placed side by side for the first time.

Applause and jubilation broke out in the operating room as the boys were separated following 12 grueling hours of surgery.

After speaking with the mother, Staffenberg, a pediatric plastic surgeon, returned to the operating room to finish the job.

At 3:15 a.m. Thursday, Carl and Clarence were wheeled out to their mother on separate gurneys.

The look on Arlene Aguirre’s face “was a combination of relief, shock and great joy,” said Connie Cornell, spokeswoman for Blythedale Children’s Hospital in Valhalla, N.Y., where the twins have been staying.

At first, doctors wanted to place the brothers in the same bed to begin their recovery.

But the mother insisted they remain side-by-side in separate beds.

“She just decided, “We’re moving on,”‘ said Dr. Steven Safyer, chief medical officer at Montefiore.

The boys were both “strong and stable” Thursday afternoon. They were moving their arms and legs, and Clarence even opened his big brown eyes to look around, doctors said.

The brothers were on ventilators, their bandaged heads covered by caps embroidered with their names.

“Two days from now when they are staring at each other, I’d like to know what’s going through their minds,” said one of the lead surgeons, Dr. James Goodrich.

He said the operation, which lasted a total of 17 hours, went smoothly, for the most part.

“The only thing that threw us a curve was the conjoining part of their brains,” Goodrich said. “You can’t take two brains that are fused together and separate them without consequences. We are hoping it will be minimal.”

Wednesday’s surgery was the latest and most dramatic of four operations the brothers have undergone since arriving here from the Philippines in October.

Carl and Clarence will remain sedated and closely monitored for infections over the next 72 hours, doctors said.

They must still undergo operations to rebuild the tops of their skulls with a combination of bone from other parts of their bodies and artificial bone. Doctors said the boys will be able to grow full heads of hair as they embark on their new lives.

News of the extraordinary feat quickly spread to the Philippines, where relatives, neighbors and even the president were praying for the boys.

“It was like a miracle,” said the twins’ uncle, Andy Aguirre. “Now they’re separated and very much alive.”

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