WASHINGTON  The Supreme Court agreed Monday to decide whether it is too late for an Alabama man to argue that the murder that sent him to death row was not a capital crime when he committed it.

The inmate, Billy Joe Magwood, shot and killed Sheriff Neil Grantham in 1979 in front of the Coffee County jail. At the time, Alabama law imposed two requirements before the state’s judges could sentence defendants to death: the commission of one of 14 listed offenses and the existence of certain “aggravating circumstances.”

The murder of a peace officer like a sheriff was a listed offense. But Mr. Magwood’s crime did not satisfy the second requirement. The question before the Supreme Court is whether he took too long to raise the argument that he could not have lawfully been sentenced to death.

Although Mr. Magwood’s lawyers challenged his sentence on other grounds over the years, it was not until 1997 that they raised the question of whether his was a capital crime under Alabama law. In the meantime, a federal judge, acting on other grounds, ordered Mr. Magwood resentenced in 1985. He was again sentenced to death the next year.