DHAHRAN, Saudi Arabia, Aug. 21 -- After a harrowing, high-speed escape across the Kuwaiti desert with Iraqi troops firing bullets at his small caravan, Houston horticulturist Edward Daly arrived here tonight, disheveled and dazed.

He was so terrified, he said, that when he finally reached the Saudi border he had to pry his fingers from the door handle of the car in which he made the perilous trip.

Daly, 57, had been in Kuwait about two months and was working on a contract to design gardens for members of the royal family. To escape, he said, he disguised himself in a white Arab robe and slipped through roadblocks in a car packed with Kuwaitis and Europeans.

When he arrived at a hotel here tonight, he dashed to the front desk and asked breathlessly, "Do you have a room for a Kuwaiti refugee?" In the hotel driveway was a dusty jeep that had followed Daly's car during the journey. Its trunk had been punctured by a bullet.

Daly said the journey from Kuwait City began about 9:30 this morning. It started with two cars, he said, "but we kept picking up more as we went across the desert." At one point, Daly said, "Iraqi solders came upon us -- a bunch of them. People were coming from all over. We said, 'Lets's get out of here.' " He said the caraven sped away, careering across the desert at speeds of more than 100 miles an hour with Iraqi troops firing at them.

Despite the Aug. 2 Iraqi invasion, Daly said he had continued to work in the gardens every day until late last week. But when Iraq ordered Americans to concentrate in hotels, Daly said, he became afraid to leave his house and began plotting his escape. Eventually, he said, he met a driver who had made 18 treacherous runs with carloads of people to the Saudi border.

Daly's car rolled into Saudi Arabia about 3:30 p.m. "I wouldn't want to do that ever again in my life," he said.