Sisters Angelina and Angelica Sabuco were undergoing an expected nine hours of surgery by a team of more than 20 doctors and nurses to gain their independence.
By mid-afternoon, hospital spokeswoman Reena Mukamal announced the girls had been separated and moved to their own operating rooms for the second phase of surgery - reconstructing the area where they were connected.
Mukamal said doctors were pleased with the progress of the operation so far at Lucile Packard Children's Hospital in Palo Alto.
Dr. Gary Hartman, lead surgeon on the case, had said keeping the girls connected carried bigger risks for their health than the separation procedure.
If one conjoined twin dies, the other will die within hours. Muscular and skeletal deformities can also worsen with time.
Ginady Sabuco, the girls' mother, has said the parents want them to live normally.
"When they argue, they can be alone. When they play, they can play together or apart," she said Monday.
The surgery required separating livers, diaphragms, breastbones, chest and abdominal wall muscles.
The reconstruction includes covering the holes that remained after the girls were separated. Surgeons had stretched their skin prior to the operation to patch the area.
The children were expected to be in the hospital for two to three weeks.
Born in the Philippines, Angelina and Angelica came to the United States with their mother last year. They live in San Jose with their parents and 10-year-old brother.
Given their otherwise good health, doctors were optimistic about a successful operation. Hartman has performed five other separations. This is the second such surgery at Stanford.
