Here on the banks of the Kennebec River, a strange thing is happening in this era of Navy ships being delivered years late and way over the original price tag.

The venerable Bath Iron Works, which started building ships for the Navy in 1890, is building a new breed of destroyer on time and under the agreed-upon price.

And, according to the shipyards's top management, Bath has no intention of filing any claims against the government for extra money -- a promise that contrasts with the $2.7 billion other shipbuilders have demanded the Navy pay them for unexpected costs on their contracts.

Why Bath Iron Works is such a bright spot in an otherwise dark shipbuilding picture -- including delays totaling 100 years -- is a story of Mainers who like to build ships, of belated Navy reforms and of a company management determined to bite off no more than it can chew.

The end result is a new class of warships -- which look like small destroyers but are called guided missile frigates with the Navy designation FFG designed to keep the sea lanes open if war should break out.

"The best ship in 20 years," enthused Rear Adm. J. D. Bulkeley after the first of this new class, the Oliver Hazard Perry, went through her seat rials after Bath Iron Works delivered her to the Navy last December.

From anaval strategy standpoint, the Perry class marks a victory for those who argue that the time has come to build smaller, cheaper ships because no single ship -- including nuclear-powered giants -- can cover two places at once.

From a political standpoint, Bath's performance on these small frigates raises the question whether this yard could have avoided the delays and cost overruns which have plagued Litton's shipyard in Pascagoula, Miss., as Litton built the Navy the Spruance class of destroyers.

The Spruance contract pitted the Maine delegation in Congress against John Stennis (D-Miss.), chairman of the Senate Armed Services Committee, who helped locate the Litton yard in his home state. Litton had no experienced shipbuilding force to compare with Bath's and ran into trouble when it tried to train one.

Although comparative figures are hard to get from the Navy, the Pentagon's fiscal 1979 report on the cost of major weapons shows that each of the new 3,600-ton patrol frigates -- including research and everything else -- was expected to cost $152 million compared to $383.5 million for the 7,300-ton DD 963 Spruance destroyer and $938.6 million for the 9,000-ton DDG-47 Aegis anti-aircraft destroyer. (All figures are fiscal 1978 estimates.)

Here at the shipyard, Navy and company executives talk differently. They focus on how much it will cost the yard to build the bodies of new class of patrol frigates. The Navy has a target price of $48 million for this construction -- not counting the cost of the engines and weapons the government will furnish -- and a ceiling price of $52.6 million.

Under the latest estimates, Bath, after allowing for inflation, will deliver the 11 ships it has contracts to build for the $48 million target price or less -- the first time a shipbuilder has done so well on a surface combatant in almost two decades.

Also, Bath executives insist they will deliver all 11 ships on the average of seven weeks ahead of schedule, saving the Navy between $20 million and $30 million.

The first of the new class, the Oliver Hazard Perry, was delivered to the Navy last December. The Perry is 445 feet long, carries two antisubmarine helicopters in hangars on the stern, is armed with missiles and a 76-millimeter gun, can steam at more than 30 knots with two gas -- turbine engines turning the single propeller, and is highly automated so a comparatively small crew of 11 officers and 153 enlisted men can operate the ship.

Bath is building the ships in sections so workers can install everything from steel decking to light bulbs in an assembly building rather than struggle to do this in the cramped quarters of the ship after it is launched.

Although other ship yards, including Litton, now build ships in sections, Bath's ability to attract and hold high-quality workers is hard to match elsewhere in the country. The Maine yard has about 10 applicants for every opening and has only about 12 percent of its 5,000-person work force leave every year, with only about half that percentage quitting.

Robert C. Upham, a 50-year-old foreman at the Bath yard, exemplifies why so many people want to work there and stay.

"I tried California right after high school," recalled Upham in an interview here, because he thought he wanted to get into aviation. "But I got so homesick for Maine out there. I like the four seasons." So he returned to Bath, took a job as an apprentice in the same yard his father was employed and has been building ships here ever since.

"It's been a good steady job," said Upham. "I've never been laid off a minute since I lived here. And it's the best-paying job around."

Capt. Charles L. Mull, the Navy officer overseeing the patrol frigate program from an office at the Bath yard, said in an interview that "we don't have an attitude problem among the workers here. They want to do it right."

Mull added that the Navy itself has instituted a number of reforms to reduce the chances of cost overruns and delays. One such reform was building and testing the lead ship before freezing the design of the others in the class. This meant a delay of almost two years between the commissioning of the first ship, the Oliver Hazard Perry, and the start of the second one. But Navy leaders contend this "fly before you buy" approach is paying off.

Another improvement made in the Perry program was "putting everybody in bed together from the beginning" so that the designs passed muster with the Navy executives who would deploy the ships and the yards that would have to build it, Mull said.

Also, an extraordinary effort was made to test extensively on land the engines, weaponry, electronics and other gear before it was put in the ship, he continued.

John Sullivan, president of Bath Iron Works, in an interview credited the yard's ability to complete 76 percent of the first production ship, designated the FFG 8, on land before launch with saving money and time.