Large plumes of smoke could be seen over the capital following the strikes Nato is enforcing a UN resolution to protect Libyan civilians, following the uprising against Col Gaddafi's rule.
But Russia, which did not back the resolution, has said the raids are a violation of its terms.
The BBC's 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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Russia foreign ministryAir strikes are not stopping the military confrontation between the Libyan parties and only creating more suffering”
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.
The anti-Gaddafi rebels are largely in control of western Libya 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 it is "in no way moving us closer toward achieving the overall goal of quickly ending the armed conflict".
"Air strikes are not stopping the military confrontation between the Libyan parties and only creating more suffering among peaceful civilians," Russia's foreign ministry said in a statement.
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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