This month Martina Hingis celebrated becoming only the fourth woman ever to occupy the number one position for 200 non-consecutive weeks.

Yesterday she was within a handful of points of a third-round defeat which could have seen her begin next month without it. Favourite for the US Open in name only, she survived a sequence of strange second-set incidents to escape with a bizarrely scrambled 4-6 6-4 7-6 win.

Majoli, whose victory in the 1997 French Open final four years ago was a career-best win, has it burned into her psyche that she has the game to to beat Hingis. Whether she has the temperament ever to do it again is more questionable.

For a set and a half, pigtail flailing, crucifix flying, ground strokes freely swinging, Majoli often overwhelmed, sometimes wrong-footed, and occasionally threatened to demoralise the top seed.

She embarrassed her Swiss opponent with pace, made Hingis's second serve seem flimsy, and reminded her that since that disastrous day four years ago Hingis's lack of weight of shot has become increasingly exposed.

"I didn't know what to do exactly," Hingis admitted.

Then, at 3-2, with Majoli threatening her third break of the match, the mood took a series of strange switchbacks. Hingis had a service fault called so late that Majoli's return had already found the net, and the argument Hingis created pounded enough adrenalin into her system to help her out of trouble.

Then Majoli became distracted by, of all things, a loud sneeze before she went to serve, pausing lengthily, laughing conspicuously and eventually delivering a double fault as she dropped the game.

It cost the Croatian the set, and a further bout of smiles when Hingis dropped her racket in the middle of a rally, contributed to a time violation warning for Majoli and the loss of her serve at the start of the final set.

Majoli immediately decided that a legitimate delay was required, getting almost 15 minutes' break as she called for the trainer to strap her playing hand and thigh.

One wondered at the mind-set which caused it and soon after that Majoli went two breaks down. But even then Hingis could not capitalise.

Twice as she served for the match Hingis's delivery was exposed as vulnerable, and it required an undignified recovery from 4-5 down in an emotionally taxing tie-break before she escaped.

"I don't know how I did it - I think maybe the crowd helped me in the end," she said.

Venus Williams got through 6-2 6-2 against Meilen Tu, an improving Californian whom she beat 6-2, 6-2 despite three times losing her serve.

Meilen means "beautiful" in Mandarin, which Tu speaks fluently, and there was fluency in her ground strokes too. But it was force not grace which mattered here.

Indeed the differences in weight and height between the 6ft 1in, 160lb champion and her diminutive compatriot made it look from the start like mismatch.

There were no sneezes but Venus's voice made her sound as if she had a cold. But even at the age of 21 she was too seasoned to admit that. "No. I'm okay," she said, flashing a disclaiming smile.

"I have a wonderful shot at winning the tournament," Williams insisted. On this evidence, she can win when below her best.