Both men have pleaded not guilty to 12 charges stemming from a heated encounter last September with two sports collectibles dealers peddling Simpson memorabilia at a Las Vegas hotel-casino.
Simpson said last fall that he put his faith in the jury system and was confident of an acquittal - a conviction could put him away for life.
"If I have any disappointment it's that I wish a jury was here," Simpson said in November, after a contentious four-day preliminary hearing in which prosecution witnesses were cast as opportunists, pimps, con artists and crooks out to make a buck off him.
"As always, I rely on the jury system," he said.
Simpson was stopped by Nevada Highway Patrol troopers Sunday on Interstate 15 south of Las Vegas after someone he spoke with at a gas station reported he appeared to be intoxicated, NHP Trooper Kevin Honea said.
"No signs of alcohol were detected, and he was on his way," Honea said Monday. "It looks like the only thing he did was be nice to somebody at a gas station."
Lawyer Robert Lucherini lost several last-ditch bids to get the Nevada Supreme Court to postpone or sever Stewart's trial from Simpson's.
He argued Stewart can't get a fair trial before a jury sure to know about Simpson's acquittal in Los Angeles in the 1994 slayings of his ex-wife, Nicole Brown Simpson, and her friend, Ronald Goldman. After the "Trial of the Century," Simpson was found civilly liable for the deaths and ordered to pay a $33.5 million judgment to Goldman's family.
In March, Clark County District Court Judge Jackie Glass postponed the trial from April until September to give the defense more time to prepare. In granting the delay, the judge acknowledged it took longer than expected for prosecutors to analyze and enhance tape recordings, transcripts and fingerprints and turn them over to the defense to prepare for trial.
Prosecutors, defense lawyers and Glass have used 26-page questionnaires to identify prospective jurors with biases and cut a jury pool of 500 to fewer than 250.
Jury selection still could take a week or longer, court officials said.
When the 12-member panel and four alternates are seated, the prosecution will tell them that Simpson and Stewart walked into the casino hotel room on Sept. 13, 2007, with four other men and robbed the sports collectibles peddlers at gunpoint of items that Simpson said had been stolen from him.
Simpson, 61 and now living in Miami, maintains he didn't ask anyone to bring guns and that he didn't know anyone in the room was armed.
The stakes are high. Simpson and Stewart have pleaded not guilty to the charges, which include burglary, coercion and assault with a deadly weapon. A robbery conviction would mean mandatory prison time. A kidnapping conviction carries the possibility of life in prison with the possibility of parole.
Four of the men who accompanied Simpson - Charles Cashmore, Walter "Goldie" Alexander, Michael "Spencer" McClinton and Charles Ehrlich - pleaded to lesser felony charges and agreed to testify for the prosecution.
But Simpson defense attorney Yale Galanter got Alexander to admit that he would have slanted his testimony in Simpson's favor if the price was right.
"Alexander offered to sell his testimony to the highest bidder," Galanter said as he prepared for trial. He promised to expose troubled backgrounds of the witnesses lined up against Simpson.
"This is a cast of very nefarious characters," Galanter said. "And the truth is, these items were not memorabilia. The law has always provided a right, dating back to our founding fathers, to recover personal property."