Florida Gov. Robert D. Graham signed death warrants today for convicted murderers John Arthur Spenkelink and Willie Jasper Darden, condemning them to die in the electric chair next Wednesday morning shortly after 7 a.m. barring a last-minute reprieve. They would be the first persons executed in this country since Gary Gilmore died by firing squad in Utah in 1977, and the first in Florida since 1964.

Spenkelink, a 30-year-old California prison escapee, was convicted in 1973 of murdering Joseph J. Szymankiewicz, 43, in a Tallahassee motel. Spenkelink claimed he killed in self-defense. The jury found otherwise and recommended the death penalty. Then-Gov. Reubin Askew signed a death warrant for Spenkelink in 1977 but a legal appeal saved him.

Darden was convicted and sentenced to death in 1974 in Lakeland, Fla., for the murder of James Turman during a furniture store robbery.

Gov. Graham's chief counsel, Robin Gibson, said Graham had determined that there is no basis to alter the court-imposed death sentences in either case.

Under Florida law, the death warrants are good for one week and must be carried out before noon Friday, May 25. State Prison Supt.D. H. Brierton set the executions to begin at 7 a.m. Wednesday.

Darden's attorney filed a request for a stay of execution with the Florida Supreme Court late today, but Spenkelink's case appears to have almost no room for further delays. Spenkelink also has an appeal pending with the court, asking that his sentence be vacated, but the court has not stayed his execution.

Florida law provides that the governor alone may sign the death warrant of a prisoner who has been sentenced to death. However, if he wishes to grant clemency, it would require the vote of the governor and at least three other members of the seven-member Executive Clemency Board, composed of statewide elected officials.

Ironically, at least three members of that Board would have voted to grant clemency to Spenkelink if the governor had so recommended. They indicated their positions privately to a reporter before Graham announced his decision.

Currently, 134 men are on Death Row at the huge and overcrowded Florida State Prison at Raiford, a small town in north Florida's farming country 40 miles southwest of Jacksonville. That's where the executions will take place, barring another last minute decision to halt them.

One member of the Executive Clemency Board who wanted to remain anonymous commented, "I want to tell you, I don't know how we're going to fry 134 people. If I were Bob Graham I would be looking for a rule of thumb to grant clemency to as many as I could. Too much rests on the governor. I voted to implement the death penalty when I was in the legislature but we're imposing it on a broader scale than we're going to be able to sustain."

Another board member, asked how he would vote if the governor recommended clemency, commented tersely, "I would support the governor." He refused to elaborate. A third member of the board said he, too, would have voted to support a recommendation of mercy by Graham and commented, "My God, man, we have over 130 men in there. We can't execute all of them. We'd have to set up gas chambers. We can't do that."