Both say they plan to come back, but it is indisputable that Wimbledon has seen the best of them. Graf, the seven-times women's champion, is 29 now, Agassi a year younger. Both of them, and Steffi in particular, have had to battle back from severe injuries and if they wanted to call it a day now, no one would be surprised.
Indeed, Agassi astonished the tennis world by climbing back last year from the depths of a 141 world ranking which obliged him to start playing Challenger tournaments to get enough points to be accepted again into events which he once won as a matter of course.
The man who became Wimbledon champion six years ago through the genius of his return of serve and who also won the Grand Slams at the United States and Australian Opens was out of shape, overweight and married to Brooke Shields. The nuptials were his best win of a 1997 tennis year which, on the court, added up to a dismal 12 wins and 12 defeats.
Then a glorious run on the early-season hard courts of America, in which he won the San Jose and Scottsdale tournaments and was runner-up at Key Biscayne, restored him to the top 25. Agassi, not the greatest lover of clay, even won a tournament on the slow stuff, capturing Munich before coming a cropper in the first round of the French Open. Now Wimbledon has pulled him lower again and he has set his sights on doing well at the US Open, where he won in 1994 and was runner-up the following year. The US Open was the event he tried hard to win again in that dismal 1997 season, only to fall in the fourth round to the eventual champion, Pat Rafter.
So what keeps him going? He certainly does not need the money, though he may have ongoing commitments to his sponsors, particularly Nike. Does it not dispirit him to suffer a thrashing from up-and-coming youngsters such as the Russian 18-year-old, Marat Safin, who knocked him out at Roland Garros? People whose sheer power tends to nullify Agassi's skilful and lovely touch? "I have to give myself a year from that low point in my career last November just to see if I can get back to my best, whatever that may be," he said. "But, right now, I feel I have more to do with some of my defeats than my opponents. So I haven't even considered giving up as an option.
"Right now I don't even consider myself close to something like that. I know all about bumps in the road, I know the feeling real well and I know the road real well. Ultimately you've got to be motivated for it and I'm certainly not out there for my health. So it could be said I'm very sincere about carrying on, it's very important to me."
As a way of preparing for the US Open, the Grand Slam which is dearest to him, Agassi plans an intensive summer playing the hard court tournaments of Washington, Indianapolis, Cincinnati and then the Canadian Open, as well as the Davis Cup.
Agassi's is an ambitious programme and one wishes him a healthy as well as prosperous time of it. It seems more than Graf would be capable of achieving in her present fragile state of health. Her coach, Heinz Gunthardt, said just before Wimbledon that, while Steffi might be looking beyond the next tournament, he certainly was not.
After that shocking loss to Natasha Zvereva of Belarus had shown just how her firepower has been blunted by the demoralising sequence of injuries and niggles which undermined her attempt to get back on the circuit after last summer's knee operation, Graf insisted she would try to "stay on track". Whether she possesses the will to carry on for much longer, particularly if she is laid low by further injury is doubtful. But she is planning some exhibition matches, followed by the San Diego tournament, before the US Open, where she won on her last two visits, in 1995 and 1996.
Asked point blank after the Zvereva match what motivated her to carry on, Graf attempted to explain that, although she had accomplished enough, she was still trying to achieve her best level of competition again. "And I don't see why I can't." But she would not commit herself to another booking for Wimbledon 1999. "It would be nice to play again and, hopefully, be in different shape and enjoy myself. But I've learned enough to take what's coming up next, so I don't know."
Margaret Court, Chris Evert and Martina Navratilova won Grand Slams after their 30th birthday. So did the likes of Ken Rosewall and Arthur Ashe on the men's side. But the likelihood of Agassi and Graf pulling it off in an era when the tennis players, like policemen, are getting younger, is sadly remote.Reuse content