The Maine attorney general's office argues that the state must protect the health of its children and that Internet and telephone sales of tobacco products have become a serious problem.

Two lower courts ruled against Maine. But if Maine officials prevail in the Supreme Court, "any number of states will impose different standards on any number of different products that they deem unhealthy or unsafe," say the three New England transportation company associations that filed suit.

Intricate national delivery networks have been able to speed $6 trillion worth of packages to their destinations every year because Congress mandated that cargo carriers not be subject to an inefficient patchwork of state laws, the shipping companies argue.

Like other states, Maine has imposed steep increases in cigarette taxes. So smokers nationwide increasingly are going online for bargains, and underage smokers are among them, according to anti-smoking groups.

A 2002 study concluded that Internet vendors sold 400 million packs of cigarettes annually, 2 percent of the cigarettes consumed in the United States, a figure that anti-smoking groups say is growing.

The number of Internet cigarette vendors has risen sharply from 88 in January 2000 to 772 in January 2006, says Kurt Ribisl, an associate professor at the University of North Carolina's school of public health who has spent the past eight years studying the issue.

"This is big business for some of the companies," said Dennis Eckhart, head of the tobacco litigation and enforcement section of the California attorney general's office. "Similar laws in several other states definitely would be at risk if the Supreme Court does not rule in favor of the state of Maine."

Ribisl says the number of Internet Web sites selling tobacco products has leveled off in recent years. At least 40 states now prohibit or severely restrict the direct delivery to consumers of tobacco products purchased from Internet vendors, state attorneys general said in a filing supporting Maine in the case. In addition, credit card companies and several major shipping companies have agreed to cease payments and cease shipping for Internet cigarette sales.

The delivery companies say they are burdened by a patchwork of widely varying state requirements.

Under the Maine statute, delivery companies must check packages against a list from the state attorney general of known unlicensed tobacco retailers. They must deliver only to the person to whom the package is addressed and a recipient under age 27 must present identification.

"Worthy motives are not enough" to uphold Maine's law, a federal judge decided in 2005.

If there is to be regulation in this area, it will have to come from the federal government, the judge ruled.