The $108,900 Delaware Handicap had been over for six minutes before jockey Jorge Velasquez met trainer John Veitch in the unsaddling area.

"Don't you know we've won?" were the Panamanian rider's first words shortly after he had dismounted.

"Frankly, I'm not sure. A lot of people around me think we've been beaten," Veitch replied.

Velasquez would not accept defeat for an answer. A minute later, when the photo-finish sign went off and the order of finish was posted on the infield board, it turned out the jockey knew how to judge the extremely close finish.

Our Mims, 3-year-old filly from Calumet Farm making her first start against older fillies and mares, defeated Mississippi Mud by the skimpiest of noses.

The victory was worth $70,785 to Admiral and Mrs. Gene Markey, whose Calumet Farm is making a resounding comeback this season, what with Our Mims the nation's leading 3-year-old filly and her 2-year-old half-brother, Alydar, bidding for the 2-year-old championship.

"Mrs. Markey and the admiral don't get out to the races any more, like they did in the old days, long before I started training for them," Veitch acknowledged. "But the tremendous interest is still there. I'm on my way now to phone them, in Lexington. The phone won't finish the first ring before Mrs. Markey has picked it up."

Our Mims is a bay filly by Herbager out of Sweet Tooth, by On-And-On. She is named for the Markeys' daughter, Melissa.

Last year, as a 2-year-old. Our Mims was winless in seven starts. Sprinting is not her forte; distance events are. The successful crossing of the Delaware today marked her third major victory, all coming at distances of 10 to 12 furlongs.

Valazquez turned in another brilliant ride to help get Our Mims' nose in front of Mississippi Mud's on the wire.The 12,997 fans had made the latter their 8 to 5 favorite, a slight edge over the 9-to-5 Our Mims.

"Jorge rode super," Veitch agreed. "He timed everything just right."

Our Mims was last as the field of five swung into the backstretch. Lucie Manet, ridden by Steve Cauthen, went for the early lead against Mississippi Mud and held a narrow advantage over the favorite until the far turn Mississippi Mud left the California filly at tha point, only to be joined immediately by Dottie's Doll.

Dottie's Doll forged here head in front briefly, at the top of the stretch, but Mississippi Mud rallied along the rial and was a half-length ahead of that rival at the eighth pole. Our Mims was in high gear by now, only a half-length farther back, on th outside.

Mississippi Mud never quit, although she was under steady pressure every step of the mile and a quarter from three foes.

Our Mims paid $5.20 straight after completing the mile and a quarter in 2:01. She carried 117 pounds, or 123 on the scale, one less than the high-weighted Mississippi Mud. Dottie's Doll held on for third money, more than two lengths behind th embattled leaders.

"The Beldame at Belmont Park four weeks from now will be Our Mims' next race," Veitch volunteered. "The distance (nine furlongs) and the date fit here perfectly. She's had two hard races in a row, the Alabama and today."

Calumet is hoping to make off with Eclipse Awards for the 3-year-old filly and the filly-and-mare division. A victory in the Beldame or the Ruffian Stakes in New York this fall would give her a solid claim to both titles. Both events are run at weight-for-age, favoring the 3-year-olds slightly.