In their unending quest for new places to grab the fast-food consumer's dollar, Burger King has joined the Navy and McDonald's has gone to school.

Burger King opened a new restaurant this week on the grounds of the Pearl Harbor Naval Station in Hawaii. The company says the restaurant, which is owned by the Navy and operated as a Burger King franchise, is the first inside the grounds of any U.S. military installation and will be a prototype for the chain's plan to take a big share of a $1 billion-a-year military food market.

McDonald's new venture is on the site of another famous battle, Lexington, Mass. The company has opened a restaurant inside Minute Man Vocational High School, which is adjacent to Minute Man National Park. This facility, said to be the first in a public school, is owned by McDonald's, operated by students in the school's culinary arts program, and open to the public.

For industry leader McDonald's and No. 2 Burger King, the offbeat locations are logical extensions of their attempts to move beyond their traditional sites at highway interchanges and suburban shopping areas into colleges, airports, parks, bus stations, truck stops and office buildings.

Both companies said these ventures reflect imaginative approaches to marketing, not saturation of their traditional areas. But some analysts of the volatile fast-food industry said McDonald's and Burger King may be reaching the point where there is no more room to grow unless they find new settings.

"The prime pieces of real estate on the highways and in the downtown areas are gone," said Michael Culp, a prominent industry analyst at Bache Halsey Stuart Shields Inc. "McDonald's has a lot of them, Kentucky Fried Chicken has a lot of them. They are remodeling their stores to make them smaller, so they can run on smaller volume, putting them in different places. We are approaching saturation, and this search for new places is a sign of it."

Timothy Johnson, director of institutional development at Burger King, said the move into Pearl Harbor and other nontraditional fast food sites "absolutely does not mean that the usual areas are saturated. This is just another prong, a new approach, another avenue of development." He said college campuses and military installations are "the two biggest areas we will be looking at" in the search for growth opportunities.

He said the Navy was determined to expand its food service to give its personnel more of what they want, and Burger King is already negotiating for restaurants at two bases on the mainland. "In the relatively near future," he said, "the chow line will be as outdated as 'From Here to Eternity' type barracks." Most of today's recruits, he said, "grew up eating fast food."

Burger King is apparently not going to have the military market to itself for very long. A spokesman for McDonald's said his company is near agreement with the Marine Corps for a restaurant at Camp Pendleton, Calif.

McDonald's already has several outlets in innovative locations: Children's Hospital in Philadelphia, the student union of Ohio State University, Miami International Airport, the Toronto Zoo. But none has stirred as much interest as its high school venture, which has received national television coverage.

Minute Man High School is a 65-acre facility with 1,200 students. The 125 students in its culinary arts program already operate a bakery and snack bar that are open to the public. Both the snack bar and the new McDonald's compete with the regular school cafeteria.

Peter Craufts, food service director at Minute Man, said it was much cheaper for the students to eat in the school cafeteria, "but when whey have a choice, about 80 percent will choose the place with a la carte items."

In deference to parental concerns about diet, McDonald's agreed not to serve coffee or carbonated drinks during school hours. Asked whether the restaurant open to the public might create security problems in the school, Craufts said, "you must have problems down there in the city that we don't have here."