A NATO spokeswoman said Sunday that Libyan leader Moammar Gadhafi's "regime is crumbling," as rebels in the Libyan capital of Tripoli said they were advancing on Gadhafi's compound.

The developments came on a night when Libyan rebel representatives claimed that rebels captured Saif al-Islam Gadhafi and Saadi Gadhafi, two of Gadhafi's sons.

Here are some of the latest developments of the fighting in Tripoli, the latest installment of battles in a months-long uprising in Libya.

[Updated at 11:24 p.m. ET, 5:24 a.m. Monday in Libya] Among the scores of rebel fighters who advanced on  Tripoli are members of the "Tripoli Brigade," a group of rebel troops who'd once lived in the capital who might help navigate the city, reports Sara Sidner. But they weren't all professional soldiers, such as one IT worker who hadn't held a gun before joining the movement a few months ago.

[Updated at 10:21 p.m. ET, 4:21 a.m. Monday in Libya] U.S. President Barack Obama has said "the momentum against the Gadhafi regime has reached a tipping point."

"Tripoli is slipping from the grasp of a tyrant," Obama said in a statement released by the White House on Sunday night. "The Gadhafi regime is showing signs of collapsing. The people of Libya are showing that the universal pursuit of dignity and freedom is far stronger than the iron fist of a dictator.

"The surest way for the bloodshed to end is simple: Moammar Gadhafi and his regime need to recognize that their rule has come to an end. Gadhafi needs to acknowledge the reality that he no longer controls Libya. He needs to relinquish power once and for all. Meanwhile, the United States has recognized the Transitional National Council as the legitimate governing authority in Libya.

"At this pivotal and historic time, the TNC should continue to demonstrate the leadership that is necessary to steer the country through a transition by respecting the rights of the people of Libya, avoiding civilian casualties, protecting the institutions of the Libyan state, and pursuing a transition to democracy that is just and inclusive for all of the people of Libya. A season of conflict must lead to one of peace.

"The future of Libya is now in the hands of the Libyan people. Going forward, the United States will continue to stay in close coordination with the TNC. We will continue to insist that the basic rights of the Libyan people are respected. And we will continue to work with our allies and partners in the international community to protect the people of Libya, and to support a peaceful transition to democracy."

[Updated at 10:14p.m. ET, 4:14 a.m. Monday in Libya] Opposition forces said early Monday that forces loyal to Libyan leader Moammar Gadhafi could be planning to re-enter Tripoli's Green Square, where scores of rebel fighters had gathered. CNN could not independently confirm the claim.

[Updated at 10:09 p.m. ET, 4:09 a.m. Monday in Libya] A CNN iReporter captured video of a massive celebration in Freedom Square at the rebel stronghold of Benghazi, Libya.

[Updated at 9:20 p.m. ET, 3:20 a.m. Monday in Libya]  The route heading to Tripoli's Green Square - where scores of rebel fighters had gathered early Monday - was "eerily quiet," with cars passing by checkpoints run by those loyal to the opposition, CNN's Sara Sidner reported.

[Updated at 9:09 p.m. ET, 3:09 a.m. Monday in Libya] Scores of rebel fighters gathered Monday morning in Tripoli's Green Square, the same place where supporters of Moammar Gadhafi had congregated for months, CNN's Sara Sidner reported. Celebratory gunfire rung out around the square, though rebels warned that snipers may still be in the area.

[Updated at 9:05 p.m. ET, 3:05 a.m. Monday in Libya] U.S. President Barack Obama has said he'll make a statement about Libya when his administration gets full confirmation of what is happening there.

[Updated at 8:57 p.m. ET, 2:57 a.m. Monday in Libya] The International Criminal Court will hold talks Monday with Libyan rebels on transferring Saif al-Islam Gadhafi, one of the two captured sons of embattled Libyan strongman Moammar Gadhafi, to its custody, Chief Prosecutor Luis Moreno-Ocampo told CNN.

Moreno-Ocampo said the younger Gadhafi's arrest was "very important" for the war-crimes court, which issued a warrant for his arrest in June on charges of crimes against humanity.

"We'll discuss tomorrow the transition of authority, how to manage to surrender him," Moreno-Ocampo said.

Saif al-Islam Gadhafi is wanted for crimes against humanity in connection with attempts to put down the revolt against his father's four-decade rule in February.

[Updated at 8:19 p.m. ET, 2:19 a.m. Monday in Libya] Pictures are beginning to emerge early Monday from Tripoli's Green Square, where Col. Moammar Gadhafi's supporters had been gathering regularly, showing those opposed to the regime celebrating the rebel fighters' inroads. Joyous people could be seen celebrating, waving the rebel flag and even flashing the "victory" sign.

[Updated at 7:33 p.m. ET, 1:33 a.m. Monday in Libya] The International Criminal Court will hold talks with Libyan rebels on transferring Saif al-Islam Gadhafi, one of the two captured sons of embattled Libyan strongman Moammar Gadhafi to its custody, Chief Prosecutor Luis Moreno-Ocampo tells CNN.

[Updated at 6:38 p.m. ET, 12:38 a.m. Monday in Libya] A rebel spokesman in Libya said Monday that rebels are in control of most parts of the capital.

"The rebel fighters are in control of most of the neighborhoods in Tripoli," said Jumma Ibrahim, adding that fighters have made it to the city's Green Square.

[Updated at 6:36 p.m. ET, 12:36 a.m. Monday in Libya] A second son of embattled Libyan strongman Moammar Gadhafi, Saadi Gadhafi, has been captured by rebel forces moving into Tripoli, a rebel military spokesman told CNN early Monday.

The news comes about an hour after the rebels claimed they captured one of Moammar Gadhafi's other sons, Saif al-Islam Gadhafi.

Saadi Gadhafi, a businessman and onetime professional soccer player, helped set up an April CNN interview with a woman who claimed she had been raped by government troops. He later told CNN that the people behind the attack should be prosecuted.

[Updated at 5:54 p.m. ET, 11:54 p.m. in Libya] Libyan leader Moammar Gadhafi has called on Libyan Arab tribes to come to the defense of Tripoli and "cleanse" it of rebel forces, warning they would be "enslaved" by Western powers if they fail.

[Updated at 5:32 p.m. ET, 11:32 p.m. in Libya] A Libyan government spokesman said Sunday that some 1,300 people have been killed in fighting within the last 12 hours. "We expect the death toll to rise beyond anyone's imagination," Musa Ibrahim told reporters.

[Updated at 5:30 p.m. ET, 11:30 p.m. in Libya] A Libyan government spokesman warned of humanitarian disaster and a "massacre" in Tripoli as rebel forces advanced into the capital Sunday, but said forces loyal to Gadhafi were holding off the attacks.

Musa Ibrahim said Gadhafi's forces were being reinforced by volunteers coming into Tripoli and "can hold for much longer." But he acknowledged that rebel forces were pushing into the seaside capital, and told CNN that "a massacre will be committed in Tripoli if one side wins."

He denied reports that Gadhafi's bodyguards had surrendered, but repeated calls for a halt to NATO airstrikes and urged peace talks. NATO for months has conducted airstrikes in Libya under a U.N. Security Council resolution authorizing force to protect Libyan civilians.

[Posted at 5:28 p.m. ET, 11:28 p.m. Libya] Libyan rebel fighters have captured Saif al-Islam Gadhafi, the son of longtime strongman Moammar Gadhafi, a top rebel official said Sunday.

The announcement from Ali Said, general secretary of the Benghazi-based Transitional National Council, came as rebel forces pushed into the Libyan capital with the support of NATO airstrikes. There was no immediate reaction from Libyan government officials to the report.

Saif al-Islam Gadhafi emerged as a leading spokesman for his father in the early days of the revolt against Gadhafi's four-decade rule, which began with the seizure of Benghazi in February.