Ten years after the attacks that felled the World Trade Center in New York and left a pair of scorched craters in the Pentagon and in rural Pennsylvania, legal fights over liability, business interruption and property damage continue.

Perhaps the most high profile of the open civil cases stemming from the events of Sept. 11, 2001, is that of the relatives of Mark Bavis, who was aboard United Flight 175 when it slammed into the South Tower of the World Trade Center. The Bavis family's 2002 lawsuit against United Airlines Corp. and Huntleigh USA Corp., the company United employed to run its security gates on the morning of the attacks, accuses the companies of gross dereliction of duty, as 14 of the 19 hijackers responsible for the attacks passed through United-controlled checkpoints.

“They didn't just fail a little; it was a wholesale failure,” said Don Migliori, a Providence, R.I.-based attorney for Motley Rice L.L.C., which is representing the Bavis family. “Not one hijacker was deterred, nor one weapon confiscated. They did nothing that they were obligated to do under federal law.”

Mr. Migliori said the case is scheduled to begin trial Nov. 7.

After Sept. 11, thousands of victims and their families entered the federally backed September 11th Victim Compensation Fund, which paid out more than $7 billion but carried with it a waiver of litigation rights against transportation agencies, the airlines and their subcontractors.

A small percentage of families refused the funds, electing instead to seek wrongful death damages against United and American Airlines, along with a slew of other companies and transportation authorities. But only the Bavis family's claim will be put to a jury, as the rest since have settled out of court. The family repeatedly has refused settlement offers from United, insisting that the airline be held accountable for its alleged security failures.

“They've put a very high premium on United taking more responsibility for what happened that day, beyond just writing a check,” Mr. Migliori said, adding that the family also hopes to expose the specific security and planning weaknesses—heretofore barred from public release—they believe contributed to 9/11 as a teachable experience for aviation and safety administrators.

“They want folks to learn from the failures of that day,” he said. “If they simply took compensation and walked away, all of this information gathered will just disappear.”

Almost all of the remaining civil cases resulting from the events of Sept. 11 stem from claims of business interruption and/or lost property.

In June of this year, Consolidated Edison Co. of New York Inc. and its insurers—including East Rutherford, N.J.-based Aegis Insurance Services Inc.—were given permission to proceed with a suit against the Port Authority of New York and New Jersey alleging negligence in the collapse of 7 World Trade Center, the third and final tower to fall on 9/11. A three-judge panel of the 2nd U.S. Circuit Court of Appeals overturned part of a federal judge's 2009 ruling that had shielded the Port Authority from Con Edison's allegations of negligence in the design and construction of the tower and of diesel fuel tanks installed later by the building's tenants for their emergency generators.

A Con Edison substation was located beneath Port Authority-owned 7 WTC tower, a 47-floor structure that also was destroyed as a result of the attack on the two main WTC towers. The third tower collapsed late in the afternoon on Sept. 11, 2001, after burning for several hours, crushing the substation.

“Con Edison's negligence claim arises at least from the Port Authority's independent duty, as owner of the leased premises, to exercise reasonable care to avoid damage to persons or property thereon,” the appeals court panel ruled.

Cantor Fitzgerald & Co., the securities trader that lost its headquarters when American Flight 11 crashed into the North Tower of the former Trade Center, is pursuing its 2004 claim against the airline and the plane's manufacturer, Chicago-based The Boeing Co., for lost property and business interruption. Cantor Fitzgerald lost 658 of its 960 New York employees in the attack, but was told in January that it could not include those deaths in its calculation of its monetary losses.

Similarly, after settling a years-long battle with his insurers over payouts from the loss of the World Trade Center complex, developer Larry Silverstein filed his own $12.3 billion suit against American and United Airlines and their security companies—as well as the agencies that run the airports in Boston, Newark, N.J., and Portland, Maine, and several partner companies to the airlines—seeking damages stemming from negligence and a failure to properly conduct security checks.

A spokesman for Mr. Silverstein's World Trade Center Properties L.L.C. said the firm's case against the airlines likely would be held until after the conclusion of the Bavis trial.