Anti-Gaddafi fighters have breached the former Libya leader's hometown of Sirte from the east for the first time, as their three-day long assault continues.
Soldiers traded rocket fire with Gaddafi loyalists as they edged from the eastern suburbs into the city.
The advance comes two days after the soldiers, loyal to the National Transitional Council, attacked from the west before retreating again.
Sirte is one of the last remaining strongholds of Gaddafi loyalists.
The BBC's Alastair Leithead, in Sirte, says civilians have been streaming out of the city - some of them were not aware that Tripoli had fallen.
Many of them were terrified, he says, having been told that rebel fighters would slit their throats if they ventured out of the city.
Our correspondent says the remaining civilians are in increasing danger, caught in the middle of intensifying fighting.
Gaddafi loyalists have been fiercely protecting the city from NTC advances in recent weeks.
The NTC troops were forced to retreat on Saturday after getting very close to the centre from the west.
Sirte is a sprawling city and much of the fighting has been conducted over a long distance, with artillery and tank shells and Nato air strikes.
Sirte and Bani Walid, about 250km (155 miles) further west, are the only two major cities still holding out against the NTC.
Fighting is continuing around Bani Walid, with one rebel commander telling the AFP news agency he expected the final battle for control to be within the next two days.
"Since this morning we have been hitting Gaddafi's forces non-stop with heavy artillery, tanks and anti-aircraft guns," Commander Mohamed al-Seddiq told the agency.
"We are facing heavy resistance, that's why we are using the heavy artillery and not sending in any infantry for now."
The NTC still has not found Col Gaddafi, who ruled the country for more than 40 years.
But several of his children and members of his inner circle have fled abroad.
His daughter Aisha fled to Algeria, and told journalists last week that her father was in good spirits and fighting alongside his supporters.
The Algerian newspaper El-Khabar reported on Monday that a group of Gaddafi supporters, possibly including Aisha, had now left the country for Egypt.
Egyptian officials have since denied the report.
Meanwhile, UN officials are warning that more care needs to be taken to secure stockpiles of weapons and other materials in Libya.
Lynn Pascoe, the UN's top political official, told the Security Council that control must be established over sophisticated arms including ground-to-air missiles and chemical weapons.
He said destruction of chemical-weapons stockpiles stopped in February when international inspectors left the country.
Last week NTC forces uncovered a stockpile of yellowcake - a powdered form of uranium ore that can be used for nuclear weapons.
