The Supreme Court said Monday that it will review whether a federal law that makes it a crime to lie about receiving a military honor violates free speech rights.

The issue adds to the justices’ recently expansive consideration of First Amendment cases. At the same time, the court said it will consider:

● Whether corporations and political organizations can be sued in U.S. courts for complicity in torture and executions abroad.

● Whether civil service laws bar federal employees from complaining in court that their constitutional rights were violated when they were fired from their jobs — in this case, because they did not register for the military draft.

In the military medals case, a sharply divided U.S. Court of Appeals for the 9th Circuit ruled this year that the Stolen Valor Act, which Congress passed overwhelmingly in 2005, was unconstitutional. The chief judge of the circuit, Alex Kozinski, said it would be “terrifying” to permit the government to decide which sorts of lies could be prosecuted.

The politically popular act was approved to deal with an apparent proliferation of people falsely claiming to be military heroes. It allows a fine and/or a six-month prison term for someone who “falsely represents himself or herself, verbally or in writing, to have been awarded any decoration or medal authorized by Congress for the Armed Forces of the United States.”

The penalty increases to a year in prison if the person lies about a Purple Heart, a Medal of Honor or another particularly high honor.

There’s no question that Xavier Alvarez of Pomona, Calif., lied. After winning a seat on Southern California’s Three Valleys Municipal Water District board of directors in 2007, he introduced himself by saying: “I’m a retired Marine of 25 years. I retired in the year 2001. Back in 1987, I was awarded the Congressional Medal of Honor. I got wounded many times by the same guy.”

None of that was true. Alvarez pleaded guilty but said he would challenge the law as unconstitutional. A panel of the 9th Circuit agreed that it was, and the full court declined to reconsider the panel’s decision.

The majority said the law was different from those protecting against fraud or punishing falsehoods told under oath. It worried about giving the government too much power over the lies that all people at some point tell.

“If all untruthful speech is unprotected . . . we could all be made into criminals, depending on which lies those making the laws find offensive,” Kozinski wrote. “And we would have to censor our speech to avoid the risk of prosecution for saying something that turns out to be false.

“The First Amendment does not tolerate giving the government such power.”

Judge Diarmuid O’Scannlain and six other 9th Circuit judges said their colleagues were wrong. He said the decision to find the law unconstitutional “runs counter to nearly 40 years of Supreme Court precedent” in which the court “has steadfastly instructed that false statements of fact are not protected by the First Amendment.”

The case is United States v. Alvarez .

The case about corporate liability involves lawsuits filed by a group of Nigerians under the 1789 Alien Tort Statute against Royal Dutch Shell. The law says federal courts may hear “any civil action by an alien for a tort only, committed in violation of the law of nations or a treaty of the United States.”

The lower courts are divided about whether only an individual may be sued under the statute or whether it extends to cover corporations.

The suit is filed by 12 Nigerians who say two Shell units were complicit in torture and executions in the country’s Ogani region from 1992 to 1995 because of their actions aiding Ni­ger­ian soldiers who carried out the abuse. The case is Kiobel v. Royal Dutch Petroleum.

The court said it will hear the case in conjunction with another, Mohamad v. Rajoub . It involves a suit filed under the Torture Victim Protection Act by the widow of Azzam Rahim, a U.S. citizen who was allegedly tortured and killed in 1995 in Jericho.

The suit named the Palestinian Authority and Palestine Liberation Organization. The U.S. Court of Appeals for the D.C. Circuit said the law allows lawsuits only against an individual who violates human rights, rather than a political organization.

The case involving the federal workers — Elgin v. Department of the Treasury — concerns four longtime government workers who were fired after investigations showed they had not registered for the draft. Three said they didn’t know of the requirement, the fourth said he registered, but there is no record.

They contended that the ban on government employment was an unconstitutional punishment and a form of sex discrimination, because women do not have to register. The lower courts are divided on whether the Civil Service Reform Act bars federal courts from jurisdiction over such claims.

All three cases will be heard next year and decided before the court’s recess at the end of June.