WHEN he faced the third round of the 1994 British Open at Turnberry only a stroke off the lead, Jesper Parnevik was rated no better than a 10 to 1 shot to capture the title. Though the bookmakers happened to be correct on that occasion, one suspects their odds would be far less generous were the situation to arise again.

Since that event of three years ago, the gifted Swede has become a competitor of international quality. The point gained rich emphasis in La Jolla, California, last Sunday when Parnevik finished joint second to Mark O'Meara in the Buick Invitational.

It lifted him above no less a figure than Tiger Woods, into second position in the US money list with earnings of $414,307 from only four events this season. More significantly, it maintained a rich vein of form which has seen the Swede finish no worse than fifth place since starting this season in the Bob Hope Classic in January.

A measure of Parnevik's burgeoning status are stunning, cumulative figures of 68 under par for his last 17 competitive rounds, including a fifth round of 62 in the Bob Hope at Indian Wells. There, he finished third behind John Cook; went on to be runner-up to Steve Jones in the Phoenix Open; was tied fifth behind O'Meara at Pebble Beach and was tied second behind the same player last Sunday.

These performances reflect the new-found maturity of a player who betrayed crippling naivete when ultimately losing to Nick Price in that eventful Open at Turnberry.

The son of Sweden's most popular impressionist-comedian, seemed to have taken a rather curious decision at the end of the 1993 season, in aiming for the USPGA Tour. As a 28-year-old, he had only one European victory to his credit at the time - the 1993 Scottish Open which he led from start to finish. But he was also encouraged by helping Sweden to capture the Dunhill Cup that year.

In the event, Parnevik finished an impressive fourth in the US. Qualifying School and opened the 1994 season with a first round of 63 in the Hawaiian Open, leading to an eventual share of fifth place. He then went on to experience reasonable success while splitting his golfing activities between. Europe and the US, as David Feherty was doing. And he out-scored the Ulsterman by finishing 26th in the European Order of Merit from only five events, while just about holding onto his card in the US by claiming 120th position from 17 starts.

Modest progress was achieved in the US in 1995, when he ended. the season in 84th place from 19 events. But he prospered in Europe where he became the first Swede to capture the Scandinavian Masters and claimed 17th position in the money list from eight tournaments.

Then came a marked change of emphasis last year. I decided to concentrate mainly on the US, with a view to building up my game for the major champion[ships," he said. But there were substantial rewards on both sides of the Atlantic, in a bountiful September.

On the first of the month, Parnevik recorded his first top-three finish in an American tournament, sharing third place behind Loren Roberts in the Greater Milwaukee Open. Then, two weeks later, he resisted a five-birdie final round barrage from Colin Montgomerie to capture the Lancome Trophy at St Nom la Breteche.

"That was a great win, mainly because of the quality of the field," he recalled. Then, after one more tournament in the US - the Walt Disney Classic in which he finished 59th - the Swede ended the season at 53rd in the money list, with earnings of $389,266.

Inherited eccentricity was evident at La Jolla last weekend in the characteristic, upturned peak to his baseball cap and drainpipe, sixties-style trousers. But the sustained quality of his play, gained Parnevik many new admirers [among the American galleries.

Meanwhile, a share of fifth place in the USPGA Championship last August, proved that he retains the necessary sparkle for the major championships.