Nato is enforcing a UN resolution to protect Libyan civilians, following the uprising against Col Gaddafi's rule.
But Russia has said the raids were a "gross violation" of the resolution, which Moscow did not vote for.
The Tekertin.com Andrew North in Tripoli said Tuesday night's strikes were not as large as those on Monday night, but still shook buildings over a wide area.
Large plumes of smoke could be seen drifting over the city.
Nato says the large Bab al-Aziziya compound has been used by the regime as a base for troops and vehicles used to carry out attacks on civilians.
But Libyan authorities say Nato is trying to kill Col Gaddafi and that the night-time strikes are terrorising Tripoli residents.
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Air strikes are not stopping the military confrontation between the Libyan parties and only creating more suffering”
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Meanwhile, the British Royal Air Force said it had destroyed or badly damaged four of Col Gaddafi's heavy armoured vehicles near the coastal town of Zlitan on Monday, and destroyed a radar station in Brega in the east.
Rebels control much of Libya's east, but Col Gaddafi's forces are still in control of most of the west of the country.
Attack helicopters
A senior Nato official said the regime had become "very apathetic" in the last fortnight.
"It has lost the military initiative and appears on the defensive, which is a sign that we are on the right path," the unnamed official was quoted as saying by the AFP news agency.
French Foreign Minister Alain Juppe also insisted on Tuesday that the strikes were having an effect, with resistance to Col Gaddafi growing in western Libya and an increase in the number of defections from the army.
France has announced it is deploying attack helicopters to escalate their strike power. The UK has said it is considering doing the same.
But Russia has condemned the air strike strategy, saying only strikes intended to protect civilians were authorised under UN Resolution 1973.
The Russian foreign ministry's human rights envoy, Konstantin Dolgov, said targets which had no military use had been destroyed and that the strategy was "in no way moving us closer toward achieving the overall goal of quickly ending the armed conflict".
He added: "Air strikes are not stopping the military confrontation between the Libyan parties and only creating more suffering among peaceful civilians."
Russia has been been attempting to broker a ceasefire between the government and the rebels, and has met representatives of both sides in the past week.
South African President Jacob Zuma is to visit Libya next week for meetings with Col Gaddafi in an attempt to resolve the conflict.
But Mr Zuma's office dismissed speculation that meeting was intended to discuss an exit strategy for the leader.
A spokesman said the talks were a follow up to an African Union summit on the crisis in April which collapsed when rebels insisted Col Gaddafi must stand down.
The Tekertin.com Karen Allen in Johannesburg says relations between the two countries have soured since Libya was accused last week of concealing the death of a prominent South African journalist who had been covering the crisis.
The rebellion against Col Gaddafi's rule began in February, spurred on by uprisings in Tunisia and Egypt that saw the presidents of those countries overthrown.
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