Nothing seemed unusual on the afternoon six years ago when Illinois state trooper Daniel Gillette pulled Roy Caballes over for driving six miles per hour faster than the posted speed limit of 65.

Gillette indicated he would let Caballes off with a warning. But as Gillette went through some paperwork, a second trooper arrived with a drug-detection dog and began to stroll around Caballes's car.

The dog reacted to the scent of drugs in the trunk, and the troopers opened it to find a shipment of marijuana. Caballes was convicted of drug trafficking and sentenced to 12 years in prison.

Yesterday, the Supreme Court heard oral arguments in the case. To be decided is whether using a drug-detection dog on a car pulled over for a traffic offense is an invasion of privacy for which police need a specific justification, or merely an aspect of modern law enforcement no more intrusive than the sniffer dogs that routinely patrol airports and bus stations.

At trial, police said Caballes's dress and demeanor fit the profile of a drug dealer. But Caballes objected that the use of the dog amounted to an unconstitutional search of his property.

Last year, the Illinois Supreme Court threw out Caballes's conviction. The court ruled 4 to 3 that Gillette had extended the traffic stop based on "nothing more than a vague hunch" that Caballes was involved in a drug crime, and that, without that unlawful delay, there could have been no sniffing of the car.

Civil libertarians say that the court must prevent police from turning every routine traffic stop into a drug investigation. A contrary ruling, said Steven R. Shapiro, legal director of the American Civil Liberties Union, would be "an invitation to racial profiling."

The state of Illinois, supported by the Bush administration, appealed the case to the U.S. Supreme Court. It argued that the justices made clear in previous cases that dog sniffs are not searches and that they require no special justification.

In 1983, the court ruled that airport authorities did not need a warrant to have dogs sniff luggage in a public section of an airport. It called the sniff "much less intrusive than a typical search." And in 2000, the court observed in a nonbinding portion of an opinion that similar logic could apply to the use of a dog to sniff a car's exterior.

"Dog sniffs are very unique," Illinois Attorney General Lisa Madigan told the justices yesterday. "They are only going to reveal the presence or absence of contraband, and this court has held that there is no privacy interest in contraband."

Dog sniffing is "a technique we want to encourage law enforcement to use," added Christopher A. Wray, an assistant attorney general representing the Bush administration.

For the most part, the justices seemed sympathetic to this position.

"This court in two decisions . . . said that a sniff is not a search," Justice Sandra Day O'Connor told Caballes's attorney, Ralph E. Meczyk. "Do you want us to reverse that?"

Meczyk replied that the "legitimate purpose" of the traffic stop in the Caballes case was "unrelated to the purpose of the dog sniff."

"Does it matter that in today's world on Capitol Hill we're concerned with terrorist attacks?" O'Connor asked. "Can they search [with dogs] for explosives in parked cars?"

Meczyk said such a search would be justified by "public safety," but the search of Caballes's car "invaded a private space that in this case . . . Caballes had a privacy interest in."

Justice Stephen G. Breyer pressed Meczyk to explain whether "there would be anything wrong with the officer himself taking a sniff," if, for example, the authorities were trying to investigate a hypothetical "great Limburger cheese robbery."

"I'm not saying you couldn't draw the line," Breyer added. "But it is a pretty tough one."

Still, the state encountered skepticism from some members of the court. Those justices seemed concerned that if the court approved the more or less random use of sniffer dogs, as in the Caballes case, that there might be no way to limit their use.

Justice David H. Souter raised the specter of police with dogs "going through every municipal garage or going up to every home and ringing the bell."

"We're opening up rather a large vista for dog intrusion," he said.

Justice Ruth Bader Ginsburg commented that "dogs can be frightening and humiliating."

"There is some association between the idea that I have a right to be let alone by the government and not having a large dog circle my car," she said.

Madigan replied that any such risk was mitigated by the fact that the public encounters dogs regularly.

For the sixth straight oral argument session, Chief Justice William H. Rehnquist did not appear yesterday, but Justice John Paul Stevens announced that Rehnquist will vote on the case.

The case is Illinois v. Caballes, No. 03-923. A decision is expected by July.