The boys, who are both 16, were pulled from the water after a large group of swimmers got into trouble around 12.30pm.
A group of seven boys, who are international students, were swimming between the flags when they were hit by a large wave and “began to struggle”.
“It’s just one of those unfortunate incidents where a wave’s come in and caught them off-guard,” Chief inspector Chris Stiles from NSW Police said.
The swimmers were pulled to safety by Bondi Lifeguards before they were treated by paramedics, including volunteers from the Jewish-run Hatzolah service.
One boy was “submerged for a period of time”, a NSW Ambulance spokesman said, and was taken to St Vincent’s Hospital in a serious condition.
He remained in a serious condition on Tuesday afternoon.
Another boy was taken to Sydney Children’s Hospital at Randwick in a serious but stable condition.
It is believed the students were not strong swimmers.
The remaining five teenage boys were wrapped in thermal blankets and also taken to Sydney Children’s Hospital by ambulance as a precaution.
Sydney Children’s Hospital was unable to give an update on the condition of the students.
The teenagers are believed to be part of a school group from Indonesia who are visiting Australia for two weeks.
Photos from the beach showed a large group of students wearing their brown school uniform and waiting as their classmates were treated.
A spokeswoman for Waverley Council, which employs the lifeguards patrolling Bondi Beach, said six lifeguards were involved in the rescue at North Bondi.
“We are still ascertaining all of the facts regarding this incident so are not able to provide specifics on today’s event,” the spokeswoman said.
“The lifeguards would like to thank all members of the public and emergency services who assisted with the rescue.”
Police said officers from the Eastern Suburbs Local Area Command are conducting inquiries into the “near-drowning”.