After Circuit Judge Robert Cates rejected the appeal by Bennie Demps, Florida's high court scheduled an oral argument for Tuesday morning.

Demps, 49, was first sent to death row for two 1971 murders. He has avoided three scheduled electrocutions in his years on death row.

Demps, a Vietnam veteran, now is condemned for the 1976 murder of a prison snitch. He's scheduled to die by lethal injection at 6 p.m. May 31.

Originally, Demps was sent to death row for the murders of R.N. Brinkworth and Celia Puhlick, who were fatally shot in a Lake County citrus grove.

The victims were inspecting some land for sale when they happened upon Demps, who had fled to the grove with a stolen safe. Mrs. Puhlick's husband, Nicholas, was wounded.

A year after Demps was sent to death row, the U.S. Supreme Court threw out capital punishment across the country, ruling death sentences had been imposed in an arbitrary way.

Demps and 96 other death row inmates were taken off Florida's death row and returned to the general prison population.

In July 1976, the nation's high court upheld Florida's new capital punishment law. And two months later, Alfred Sturgis was fatally stabbed in his prison cell.

Before he died, Sturgis told a guard that Demps and another inmate had held him down while a third stabbed him. Demps was sentenced to death in 1978.

Since his second death sentence, Demps has survived three death warrants - in 1982, 1987 and 1990 - by winning last-minute appeals.