Tim and Tom Gullikson, the rapidly improving identical twins of pro tennis, have caused many people to suspect an attack of double vision. But consider the psychic harm they inadvertently inflicted on a German pro named Karl Meiler.

Meiler lost to Tim in the first round of a tournament at San Jose, Calif., this winter. A fortnight later, he came up against Tom in the third round of the U.S. Indoor Championship at Memphis.

Meiler did not know that there are two 25-year-old Gulliksons from Onalaska, Wis., who are virtually indistinguishable except that Tim is righthanded, Tom a lefty.

"When we started to warm up. I couldn't believe my eyes," recalled Meiler. "When he beat me in straight sets, I was very depressed that here was a player who could beat me using either hand."

The Gulliksons - bright, agreeable and promising - have made a big hit here during the first week of The French Open championships. Tim lost in five sets to top-seeded Ilie Nastase on the center court of Stade Roland Garros Thursday. Tom lost to Frenchman Patrice Dominquez this afternoon, 6-3, 6-1, 6-1.

"We are a bit unusual hard the the last couple of years because we started pretty far behind," said Tim, explaining that they only played local and state tournaments as youngsters and never entered national junior competition.

"We're basically self-taught. We grew up across the street from LaCrosse State University in LaCrosse, Wis. They had eight cement courts and a backboard. Thirty steps out the front door and we were there. But the only real coaching we've had has been in the last year, from a guy named Hank Jungle."

The twins are two of the four children - sister Sue is 28, brother Gary, 7 - of an Onalaska barber.

"My dad's a pretty cool guy," said Tim. "He plays tennis at the local high courts. I gave him my warmup jacket that says 'Gullikson' across the back. Now he thinks he's a real stud."

The Gulliksons didn't even think about playing on the pro circuit until they were 22. They both were graduated in 1974 from Northern Illinois University, where they majored in physical education. They were starting guards on the basketball team as freshmen, but subsequently gave up that sport in favor of tennis.

Tom stayed on at Northern Illinois as varsity tennis coach for one year, then took a club teaching job at Crystal Lake, Ill., outside Chicago. Tim became a teaching pro in Dayton, Ohio, where he met Jungle, who was stationed there in the Air Force. It was Jungle who convinced the twins to try the tour.

"I was teaching tennis and my wife, Julie, was teaching school, and between us we saved quite bit of money," said Tom, who has a slight gap between his front teeth and is five lighter than Tim at 5-foot 11 and 170 pounds. Physically, those are about the only differences between them.

"I wanted to support myself on the circuit without a sponsor. I started in satellite tournaments, did well and got into the Grand Prix four months ago."

Tim and his wife Rosemary - she was a sorority sister of Julie's at Northern Illinois, and set her up with Tom on a blind date - have been traveling the international tour for a year. The 1976 French Open was Tim's first Grand Prix tournament, and his best win to date was over Roscoe Tanner in the Washington Star International last summer.

Though Tom has been in major competition only four months, he already has been in the semifinals of three Grand Prix events - $50,000 tournaments at Dayton and Hampton, Va., and the $175,000 U.S. Indoors.

He is 16th in the Grand Prix standings and 59th in the computer rankings of the Association of Tennis Professionals. Tims is 103d.

"Actually, I was able to help him a lot breaking into the circuit, showing him the ropes. It's like a minor leaguer coming into the majors. You can't be worried or intimidated by the names. You've got to ignore the reputations and break the game down to its mechanics, look at each player's strengths and weaknesses.

"Just because a guy is named Nastase doesn't mean he's invincible. He still has a very attackable backhand, for instance."

Both twins have compact, fundamentally sound strokes and are heady players, constantly analyzing opponents and devising strategies to attack them. They also help each other, watching intently during matches, going over them afterward.

"They seem to play better when the other's watching," said Julie Gulliksons. "It helps Tom emotionally that I'm there, pulling for him 100 per cent, but I really can't do much for his game. Tim can spot things right away and help him technically."

The twins started tennis together and are constant practice opponents and doubles partners.

"My mother was pulling her hair out with two wild 5 year-olds on her hands, so she took us across the street to the tennis complex at LaGrossee State, which had a 25-foot fence around it," Tom said.

"She knew she could put us in there and there'd be no way we could get out. It gave her a couple of hours of peace. We chased balls for the kids in the recreation program there and then began playing ourselves. That's how we got started."

Now the Gulliksons have moved people to dust of the names of Willie and Ernest Renshaw and Wilfred and Herbert Baddeley, the most prominent sets of twins in tennis history.

The Renshaw won the Wimbledon doubles title seven times between 1880 and 1889, the Baddeleys four times between 1891 and 1896. Willie Renshaw also won the singles title seven times, Ernest once, and Wilfred Baddeley three times.

Another turn-of-the-centry English set of twins, the Allens, won a number of tournaments, but none of the majors. The most recent twins in international tennis, before the Gulliksons, were Marin and Gogu Viziru, who played Davis Cup for Romania in the late 1940s.

Now the Gulliksons are looking forward to playing Wimbledon together for the first time, and inevitably turning more heads. With their spouses they make a merry band, this foursome on ao round-the-world double date.

"We have our little arguments now and then and get on each other's nerves occasionally, as you do with anybody you're with 12 months a year, but on the whole we all get along great," said Tom.

Or was that Tim?