The top five car rental franchisers in the United States? Easy. Hertz, Avis, National, Budget and . . . Ugly Duckling Rent-a-Car?

According to Forbes business magazine, the Tucson-based corporation is one of the fastest-growing companies in the nation. And with more than 500 outlets in 41 states and Canada, including nine in the District of Columbia, Maryland and Virginia, founder Tom Duck Sr., 71, is predicting there will be Ugly Duckling outlets in more cities than Hertz and Avis by 1988.

The main reasons for this boom, according to Duck: Staying away from airports. While the Big Four go after the 80 percent of the rental business that comes from airports, Ugly Duckling is concentrating on "the 20 percent of the population that wouldn't fly for anything."

Also, says Duck, "hotels usually provide free pick-up service at airports for guests. So why start renting a car several hours before you actually need it? You can get a free, comfortable ride to your hotel, without getting lost, and the next morning, when you need a car, you can get one."

Attracting women customers. Forty percent of Ugly Duckling's rentals are to women (who make up less than 10 percent of all new-car rental customers).

Accepting cash-only customers. "If the money is coming from an individual's pocket," says Duck, "they have no trouble renting from me."

Maintaining low prices. Ugly Duckling's rental cars range from this year's models to 10-year-old vehicles. They go for $6.95 a day up to something over $20 a day.

"We have four basic criteria for our cars," says Duck. "Our cars have to look nice on the outside; be neat on the inside; start every time you turn the key; and stop every time you put on the brakes."

Duck says his cars have to be reliable. "When you're renting a car for $10 a day, three days' rental, you lose money (and a customer) if the car fails to start and you have to pay a tow truck $35 to bring it in for repairs. There's no free lunch in the rental car business."

Duck started his company in 1977, after a 25-year career in the insurance business. He, his wife and son, Tom Jr., now 38, bought nine used cars for $10,000, added another from their own driveway, and away they went. "We rented and picked up and delivered, did everything by ourselves for the first month."

Now, Ugly Duckling franchises can be found at new-car dealerships, car washes, body shops, truck and trailer rental outlets. About 10 percent are in business by themselves.

After calling Ugly Duckling's national reservation number (800-THE-DUCK), customers are transferred to the location they'll be renting the car from. "There's none of this 'We'll do our best to get the model you want,' " says Duck. "You'll know just what cars are available and what you'll get."

Duck is fond of quoting his son when asked to predict Ugly Duckling's future: "There's always room for mammals in a dinosaur age."