This is a story about an insurance company and a rating company and the struggle between them over principle and public image.

The insurance company is the Gov-(Geico), which last was rescued from collapse when stockholders and a consortium of other insurance companies stepped in to keep the Washington-based firm alive.

The rating company is the A.M. Best Co., a venerable grader of insurance company soundness. Its ratings make and break.

The problem is this: Despite a recovery plan for Gieco which many have applauded, and despite three quarters of increasing profits at Geico, Best has given the firm a "deferred" rating and insists that grade will stick for at least three years.

The rating, of course, is not good for business, though Geico officials say their company is coping well enough under it. Auto policies, by far Geico's predominant line, have not been affected because most customers are not influenced by company ratings. They shop for price and service.

Where the ratings do make a difference is in the sale of homeowners policies. Some mortgage companies and thrift institutions require customers to take out policies above a certain minimum grade and have been asking people to secure insurance from a company other than Geico.

"Some companies accept Geico, some don't," said William Behrens of Behrens Realty in Herndon. "It has to be hurting their business."

Geico officials don't like to emphasize the damage done. The company's homeowners line did suffer a reversal in 1976, dropping 14 per cent in premiums written over the previous year. But that, said a Geico spokesman, probably was due more to adverse publicity about the company's financial difficulties than its poor Best rating.

"There have been losses as a result of the rating," the spokesman said. "But the vast majority of companies are still accepting our policies, including the Federal National Mortgage Association."

Traditionally, Geico's homeowner's line has comprised only 5 per cent of its business. But a major objective of the company's recovery plan is to redistribute its business away from auto insurance and into more homeowners policies. To this extent, Best's rating is particularly nettlesome for Geico.

Top officials at Geico have written to, phoned and conferred long hours with Best's raters about receiving a better grade.

"We're unhappy and dismayed," said Thomas Exarhakis, vice president for communications at Geico. "But we're certainly not going to fold our tents and steal off into the night."

For the public record, anyway, the people at Geico have decided to the noncombative, almost complacent, about the matter. They say they are understanding of Best's position.

Best's position is, simply put: We're a venerable rating company and we can't let our rating of a company bounce up and down from year to year.

"We don't do anything to hurt any company," said Robert Schaeder, a Best vice president knowledgeable about the discussions. "I have a great deal of sympathy for Geico. But still and all, you have to be fair. We've adopted a uniform procedure and that procedure has been applied to Geico as it has been to hundreds of other insurance companies."

Best's rating formulas are very complex, the sort of formulas only a company which has been in business 78 years could have devised. Actually, Best gives two ratings. One is called a "financial category"; the other is a "policyholder rating."

Geico has been placed in Best's highest financial category, number 15. Its policyholder rating is the one that's been deferred.

The financial category number merely indicates the size of policy-holder surplus, and is not nearly as significant as the policyholder rating reflecting such factors as company management, quality of service, the firm's reserve system and more.

Geico tried to get Best to apply a slightly different measure. "What happened to us was, after all, unusual," said Exarhakis. "We thought maybe they should have taken an unusual approach."

The approach Geico suggested would have given the company credit for such unique aspects of its recovery plan as reinsurance agreements with 27 other insurance companies covering 25 per cent of Geico's business, or a vigorous management program called "Operation Bootstrap."