William Morris senses that he and son Billy have reached the pinnacle of mental and physical fine-tuning necessary to win the Equitable Family Tennis Challenge's father-son doubles competition at the U.S. Open in Flushing Meadows, N.Y., this week.

"I've always thought that a father-son team reaches its peak just as the son starts getting better than the father - as well as reaching a certain maturity level," says the elder Morris. "If I'm correct, this is our year."

On Thursday, and they hope Friday, the Morrises will be pitted against 15 other father-son finalists coming from as far as Hawaii and Puerto Rico. The tournament started with 256 local events and 140,000 competitors including all combinations of parent-progeny doubles. The Morrises are the Mid-Atlantic champions, having beaten contestants from the District of Columbia, Maryland, Virginia and North Carolina.

William Morris says he has read of complaints by such professionals as Bjorn Borg about the extreme quickness of the courts.

Morris does not share Borg's worry. "We'd rather play on fast courts. They are to our advantage," Morris reckons.

"We hit harder and are a bit less steady than some of the other teams."

The Morrises have strung together a chain of victories mainly on hard courts - including conquest of former Wimbledon champion Dick Savitt and his son.

The senior Morris, president of a commercial real estate firm, was captain of the tennis team at the University of Virginia and was ranked among the top 10 amateur players in the Mid-Atlantic states.Billy Morris, 18, is captain of the Landon School team in Bethesda.

A major key to their success is the unusual court relationship of the two William Morris says most father-son teams are quick to scrap when their play starts to fall apart. Not the Morrises. They rarely play family feud between baselines.

"We're more like two men - a couple of friends," says the senior Morris. "We have mutual respect and we're at ease with each other. We don't fight. After all, we've been playing together all of Billy's life."

The long association has evolved into telepathic coordination on the court. The two react to each other's thoughts.

While the Morrises refrain from flagellating each other during matches, they put a Vince Lombardi emphasis on making sure the results are favorable.

William Morris looks ahead to more of the thrill of victory with his 12-year-old son John, "quite a good little tennis player." Morris speaks of his wife Ann and daughter Paige as being tennis players, "but only socially."

Both the socialities and the competitors in the Morris family will be heading to New York with the enjoyment of free rein at the U.S. Open on their minds. But with ultimate truth, William Morris says, "We're not in this just for fun."