The lead surgeon, Robert Keating, said "Things are going well. We feel optimistic about the preservation of neurological function."
However surgeons have decided not to separate the twins' shared tailbone temporarily because it provided more stability to surgeons as they repositioned the boys.
Keating said that the surgery to separate the spinal cord of Mateo Asher Shaw and McHale Twain Shaw, conducted at Children's National Medical Center, took about six hours.
The next step that is planned is the separation of the boys' muscle, tissue and gastrointestinal systems, a procedure that is expected to last about four to five hours. Following this Keating said that reconstruction would then take about two to three hours more.
The twins were born on May 10 joined at the lower back with conjoined spinal cords.
Keating said, "The boys have been doing well. They're stable. So far, everything is a go. It's going as expected - which is good. We're pleased at this point. But obviously we still have a lot more to do."
The surgery which began on Wednesday morning is expected to last 14-23 hours. According to Keating he hopes to have it finished by Wednesday night.
The boys' parents, from Sheboygan, Wis., have been spending this time in a hospital waiting room. The boys' mother, Angie Benzschawel, 25, said, "It's been a roller-coaster. You have a mix of every emotion possible - pretty much the worst feeling."
Benzschawel said, 'We've been here since April. The hospital staff is almost like another family. We couldn't get through it without them.'
Over 65 people are working on the operation, including doctors, nurses and staff.
Conjoined twins occur about once in every 50,000 to 100,000 birth and only about 20 percent survive to become viable candidates for separation.