Lloyd's expects settlements to take more than five years
Experts estimate it could take more than five years for the more complex World Trade Centre claims to be finally settled.
Lloyd's has so far paid out £1.4bn, or about 23%, of what had been claimed by the end of last year.
But one senior Lloyd's figure told Insurance Times that though the hull losses were paid quickly, claims for business interruption will "clog up the courts" for years.
"There will be some workers' compensation [similar to employers' liability] and public liability cases which will still be ongoing when half of this market goes into retirement," he said.
Over in New York, the state's insurance department calculates that claims totalling $16.7bn (£10.6bn) have been paid so far.
This is a third of the estimated total insured loss of $50bn (£32bn).
But the remaining two thirds includes many complicated claims that are the subject of litigation.
Neil Coulson, a partner at accountancy firm Littlejohn Frazer, said it could be years for some of the cases to be settled.
A spokesman for New York state insurance department said it was not pressurising insurers to pay up - yet. "We want them to take their time to determine what the losses will be. We are generally pleased with the way the insurers have been reacting so far."