More than a year after Volkswagen's use of illegal "defeat device" software in diesel cars came to light, the company is close to achieving a settlement with regulators and customers for the majority of affected cars.

A settlement for the 482,000 affected VW TDI cars equipped with 2.0-liter 4-cylinder engines received preliminary approval at the end of July.

But the settlement cannot be implemented until it receives final approval from a federal judge.

DON'T MISS: Virtually all VW diesel owners will take settlement terms for 2.0-liter TDI cars

Last Tuesday, U.S. District Court Judge Charles Breyer said he was "strongly" inclined to approve the settlement, and that a final decision would be made before October 25, according to Bloomberg.

Breyer also indicated that he plans to approve a settlement with Volkswagen's 652 U.S. dealers to cover damages related to the diesel scandal, scheduling a hearing for January to consider final approval.

As with other, similar settlements, VW is admitting no liability in signing the agreement for 2.0-liter TDI cars.

2014 Volkswagen Beetle TDI

2014 Volkswagen Beetle TDI

The settlement gives owners the choice to take a buyback, or wait to have their cars modified to comply with emissions standards.

So far, though, neither the U.S. Environmental Protection Agency (EPA) nor the California Air Resources Board (CARB) have approved such modifications.

There is no indication when any modifications will be approved; it's also not clear that modification will be feasible for all cars.

ALSO SEE: Why VW diesel buyback pays owners to keep their cars for two more years

Given the potential cost of modifications, analysts have questioned whether it would be economically feasible to modify some of the older cars.

Owners have also expressed concerns about how modifications might affect their cars' performance and fuel economy.

The majority of owners are expected to take buybacks, although not all of them are happy with the terms.

2010 Volkswagen Golf TDI

2010 Volkswagen Golf TDI

Some owners want the full purchase price of their cars refunded, but the settlement only calls for them to be paid an amount based on the value of cars at the time news of the diesel scandal broke last September.

It's also expected that some owners will not take the settlement, and may sue Volkswagen individually.

MORE: Audi V-6 diesel talks 'progressing well' for October agreement, exec says

However, the majority of 2.0-liter TDI owners are now at least signed up to participate in the settlement, although they may not ultimately take the buyback-or-modification offer.

Earlier this month, Elizabeth Cabraser—lead plaintiff's attorney in the settlement—reported that only 3,298 affected owners had opted out of registering with Volkswagen for the settlement.

2014 Volkswagen Passat TDI

2014 Volkswagen Passat TDI

That works out to roughly 0.7 percent of owners.

Volkswagen must also address the 85,000 TDI models with 3.0-liter V-6 engines that have "defeat device" software.

A settlement for these vehicles would likely be similar to the 2.0-liter settlement, with offers of buybacks and modifications.

The 3.0-liter TDI models won't be discussed again until a hearing next month.

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