JUST ABOUT every Washington correspondent has a John Wayne story. I have never written mine, and this seems the best possible time to do so, with the recent passing of the "The Duke."

It happened in Miami Beach during the 1968 Republican National Convention. I had put out a special convention issue of Look magazine, for which I was then Washington editor, and, with the issue on the newstands as the convention opened and no deadline for two weeks, I had virtually nothing to do.

My only specific assignment was to keep an eye out for Nelson Rockefeller's chances for the presidential nomination and report on them to Rocksfeller's close friend and boss, Gardener "Mike" Cowless. Other than that, it was playtime, and in a wonderful corner suite at the Fontainebleau, the convention headquarters hotel.

My wife and I were in one bedroom and Look's Washington photographer, Stan Tretick, and his own wife were in the other. A kind of sitting room-rec room, with a huge bar, was on the corner between us. There was a balcony, of course, and the view from, the 10th floor was just fine - ocean, beach, swimming pool, the whole megillah.

We poured every night. Our guests were fellow newspeople and conventioneers. One regular was Leo Morrison, a most marelous man to be with. Leo was jockey-size, 5 foot 2 if he stood up straight and pushing 105 pounds. He talked out of the side of his mouth, nasally, rapidly-fire, in a Bronx-cum-Hollywood accent, and he came by that naturally because he had made its mark as a theatrical agent.

Paul Garvey, the great international correspondent who, unhappily for his readers and listeners, has since retired, introduced Leo to us in Washington. My first reaction was that the little fellow (he was 72) was a 14-carat phony - fascinating storyteller, tireless namedropper, witty and full of devilment, charming and probably harmless.

And then one night in Paul's apartment, where Leo was staying on the cuff, being then down on his luck, he brought out his scrapbook. There could be no doubt of his authenticity. Letters, notes, photographs, yellowed newspaper clippings, entire Hollywood gossip magazines - all give incontrovertible evidence that in the view of Hedda Hopper and Lolly Parsons and many a movie mogul, our little Leo had been a very big men in Hollywood. Among other surprises: he had won his airline pilot's license in 1925, and he had managed Spencer Tracy and John Wayne, among others.

"I made Wayne and then I lost him, to a woman," Leo told us, fondling brittle clips about him and the Duke. "his real name's Morrison, same as mine, and he had a sissy first name, Marion."

And out came the tale of two Morrisons: Leo managed Wayne when the Duke was making quickie Westerns at $400 a week. Leo and John Ford were good friends and agreed Wayne would be perfect as the Ringo Kid in "Stagecoach", which Ford was to direct. But the producer insisted on established star, such as Gary Cooper, until Leo in exasperation, burst out: "At least test him! I'll pay for the test!"

That he did, to the tune of $5,000. But he and Ford coached Wayne remorselessly so that, when he took the test, he got the part hands down. The picture has been a classic since its release in 1939, and so has Wayne.

"And then the big so-and-so made a picture with Marlene Dietrich," Leo said. "They became so close and she talked him into ditching me and signing up with her agent. I sued Wayne and collected $40,000 and we haven't laid eyes on each other or talked since, and that was over 20 years ago.

At the Republican convention in Miami Beach, Leo was pacing up and down on the 10th floor balcony outside our suite, his tiny frame buffeted by guests of a strong ocean breeze. Leo was pacing mostly because that very morning John Wayne had opened the convention with a rousing, characteristically patriotic stemwinder of a speech. Wayne's prescence in the same city, the same hotel, after all those years, bothered him. And Paul, who had been out on the town with Wayne the night before, was pressuring Leo to go down to the main dining room and make up with him.

Paul and the rest of us finally had Leo convinced, after several belts. We all trooped after him, like overgrown kids after a leprechaun.

In the dining room, Wayne was sitting with his back to us as we entered. Leo walking right up, slapped him on the hip, and then said, "Hi, you big so-and-so!"

Wayne looked over the wrong shoulder and saw nothing. Puzzled, he looked over the right shoulder and saw nothing. And then he looked down.

"Leo!" he shouted, with the celebrated grin breaking out. He leaped up, all 6-4 of him, and grabbed Leo in a bear hug that caught him somewhere around the ears.Leo's nose was jammed into the Duke's belt buckle.

They stayed like that a long time. Wayne kept saying, "You old son-of-a-gun!" His eyes glistened, and so did Leo's.

A blue-haired woman in a puckered pink blouse and aquamarine bullfighter's pants tugged at Paul Garvey's elbow. She shoved a notepad and a ballpoint pen at him.

"Get me John Wayne's autograph," she ordered. "Sure," Paul said. "Which one is he?"