The Associated Press

OMAHA, Neb. — Michael Phelps just missed setting another world record at the U.S. Olympic trials.

Natalie Coughlin and Aaron Peirsol showed him how to do it.

Racing about 10 minutes apart, Coughlin and Peirsol broke their own marks in the 100-meter backstroke Tuesday on another lightning-quick night at the temporary pool in America’s heartland.

Their records were the fifth and sixth of the meet — with five days to go. Both Coughlin and Peirsol were wearing the Speedo LZR Racer, which upped its tally of world marks to 44 since debuting in mid-February.

‘‘I’m really glad that I stamped my ticket to Beijing. I got that over with,’’ Coughlin said. ‘‘I feel like a huge weight has been lifted.’’

Phelps made a dogged run at perhaps the most impressive record on his staggering resume, the time of 1 minute, 43.86 seconds from the 200-meter freestyle at last year’s world championships. He was right on pace as he powered toward the wall, but he touched with only the third-fastest time in history, 1:44.10.

Then it was time for Coughlin and Peirsol to shine.

Coughlin became the first woman to break 59 seconds, just one day after she reclaimed the world record in the preliminaries. She touched in 58.97, locking up the first of perhaps as many as six races she could swim in Beijing.

Peirsol showed he’s still king of the backstroke, beating a strong field and his own record in the 100 back at 52.89, ahead of the 52.98 from last year’s worlds.

Six-foot-8 Matt Grevers took second just ahead of Ryan Lochte, who dropped a spot in the 200 free final — and another chance to race Phelps — to give himself a better shot to qualify in the backstroke. The move didn’t pay off; Lochte came on strong over the final 50 but touched in 53.37, behind Grevers’ 53.19. Randall Bal, the fastest qualifier in the semifinals, settled for fourth in 53.45.

‘‘That was probably the best field I’ve ever been in,’’ said Peirsol, one of the Nike-sponsored swimmers who ditched their regular suit to wear the LZR Racer. ‘‘I don’t think the Olympic field will be any harder than that.’’

Lochte will remember it, too, though he didn’t bother to share his disappointment with the media. He walked right past reporters and never came back.

‘‘He’s got other races, and I’m sure he’s trying not to get caught up in this one,’’ said Phelps, who beat Lochte in the 400 individual medley when they both went under the previous world record. ‘‘He’s trying to move forward.’’

Phelps returned to the pool about 50 minutes after the 200 free, posting the fastest time in the semifinals of the 200 butterfly at 1:54.02. He’ll head to Wednesday’s final as a big favorite in yet another event which has his name at the head of the record book.

As for the 200 free, one minor mistake probably cost him a new record.

‘‘The only thing I was not happy with was the last turn,’’ Phelps said. ‘‘That’s something little I can fix between now and Olympics.’’

Coughlin, who won five Olympic medals in Athens, will surely be one of the biggest stars of the powerful U.S. swimming team, along with Phelps and Katie Hoff.

A day earlier, Coughlin watched her world record in the 100 back snatched away by Hayley McGregory in the prelims. Two minutes later, Coughlin took it right back. Twenty-four hours later, she went even faster.

‘‘I knew I could go a 58,’’ she said.

After briefly holding the world record, McGregory failed to even qualify for the Olympics. She finished third in the final, edged out by Margaret Hoelzer’s time of 59.21. McGregory touched in 59.42.

On a busy night, Coughlin also qualified third in the semifinals of the 200 individual medley, an event her coach persuaded her to swim only a week ago. She has another of her strongest events, the 100 freestyle, still to come and figures to be a key member of all three relay teams in Beijing.

But no one — not even Phelps — is swimming more than Hoff. She had four more races Tuesday, competing in the prelims and semis of the both the 200 freestyle and 200 IM.

She was the top qualifier in each. In Wednesday’s final, she’ll try to add the third and fourth races to her Olympic schedule.

In Tuesday night’s other final, Jessica Hardy earned her first trip to the Olympics by winning the 100 breaststroke. The 21-year-old was under world-record pace at the flip but faded on the return lap. Still, she managed to win in 1:06.87.

Megan Jendrick, who won two golds at the Sydney Olympics as Megan Quann but just missed making the team four years ago, claimed the expected second spot for Beijing in 1:07.50 — one-hundredth of a second ahead of Tara Kirk.

Three-time Olympian Amanda Beard missed her first chance to get back on the team, finishing sixth in 1:08.80. She also failed to advance from the semis of the 200 IM, leaving the 200 breaststroke as her last opportunity to make a fourth Olympic team.