Agents representing the Schaumburg, Ill., office of an unusual Swedish insurance firm ask the typical nosy insurance-type questions of customers seeking to protect their cars or homes.

But they pay particular attention to answers to one question: ''How often do you have a drink?''

If the reply is ''only occasionally,'' or ''once a year on New Year's Eve,'' Ansvar America Insurance Co. will send your business elsewhere.

It is a business strategy based on a social crusade -- and one, incidentally, that has created an insured pool of potential claimants that company officials describe as ''conservative,'' ''responsible'' and ''risk-averse.''

In a business that depends on the accurate calculation of risk, those are soothing words.

So Ansvar says it can offer premiums to self-proclaimed teetotalers that are roughly 5 percent less than those of competitors.

Founded in 1932 in Stockholm by a group of businessmen concerned about the social costs of alcoholism, Ansvar General set up its wholly owned U.S. subsidiary in 1983 by buying a small Chicago area insurer, Central Security Mutual Insurance Co. Ansvar's U.S. headquarters are in an office building near in the Chicago suburb of Schaumburg.

Ansvar, whose management staffers are nondrinkers, sells its policies through independent agents, who also are teetotalers, in the Midwest and Arizona.

''Our feeling is that there's a problem with alcoholism in the world,'' said Ansvar America President Manus Sweetman. ''We weren't looking to only write insurance for reformed alcoholics, but to encourage young people never to pick up a drink.''

On the business side of that social question, Sweetman sees opportunity. ''We try to do our own surveys, and we've estimated that 18 percent of the population in Illinois are nondrinkers,'' Sweetman said.

The people who make up that group -- a conservative, mostly middle-age, responsible lot -- are good risks for an insurance underwriter. Ansvar, which believes it sells policies to about 3 percent of that nondrinking group in Illinois, would like to increase its market penetration to 10 percent by the end of 1992, Sweetman said.

But Ansvar's burst of growth in the United States, primarily in its other major business area, Arizona, caused three years of losses for the company and forced a re-evaluation last year of its expansion plans.

Intensive marketing efforts by Ansvar in Arizona generated sales of policies to an estimated 17 percent of the state's nondrinking population, Sweetman said. That's an enviable penetration level for any insurer. But the policies were priced too low, Sweetman acknowledges.

Ansvar America last year reported a $2.9 million underwriting income loss on premium income of $11.7 million. A $6 million cash infusion from the parent firm was required to bring the subsidiary out of the red, according to documents filed with the Illinois Department of Insurance.

''Initially, we expanded into other states faster than we took advantage of the states we were already in,'' said Sweetman, who took over as president of the U.S. subsidiary a few months ago. The company plans to concentrate on expanding its business in states where it has a strong base, particularly Illinois, as well as Missouri, Wisconsin and Indiana.

Sweetman said Ansvar America expects to break even or report a small profit in 1990. ''We are expected to be self-sustaining, and we probably will be,'' he said.

By most standards, the company is small, with 19,000 policies in force in the United States, including 6,000 in Illinois and 5,000 in Arizona. Worldwide, Ansvar General has 690,000 policies in 13 countries, including Sweden, Norway, the Netherlands, United Kingdom, West Germany, Japan and Australia.

Though other major U.S. insurers, particularly life insurance companies, have succeeded in niche marketing by offering discounts or special policies to nonsmokers, few offer discounts or policies to nondrinkers.

One that does, however, is Sentry Insurance, a Stevens Point, Wis., firm. For the last five years, it has offered a ''payback'' policy to drivers who sign a waiver saying that if they or a driver of their car are intoxicated and involved in an accident, they forfeit their right to collect for damage to their car. Any health costs or costs to repair the other vehicle, are covered, said Dan McGinnity, corporate communications manager for the firm.

In return, policyholders who avoid accidents for five years are entitled to a refund of half their first-year premium payment.

As the company approaches its first payback period under the policy, 91 percent of the 20,000 policyholders still with the company are eligible for a refund, McGinnity said.

''Every insurer has a good-driver discount,'' he said. ''No other insurance company provides a deterrent to people not to drink and drive. If you're the type of person who drives after a few drinks, you'd be hesitant to take out this policy, because you're jeopardizing your collision coverage.

''We couldn't or wouldn't offer half the premium back if we didn't think these policyholders would be better drivers,'' he said. The policy is available in Wisconsin, Illinois and 13 other states.

He noted one New York study that estimated that 50 percent of every consumer dollar spent on car insurance is paid for alcohol-related accidents.

Much of Ansvar's literature contains similar wisdom, opining that ''the person who chooses not to drink alcohol is careful and economical, given to taking exercise, is diet-conscious and displays social responsibility and human solidarity, high ideals and religious commitment.''

Applicants who seek insurance with Ansvar sign statements saying they are teetotalers. Enforcement is based on an honor system.

If Ansvar finds out the insured is drinking, it will not renew the policy, Sweetman said.

Sweetman said agents do not ask why an applicant abstains from drinking but simply whether he or she does. That means a reformed alcoholic could receive insurance just as easily as a person who declines drink on religious grounds.

''Insurance is based on the belief that 95 percent of your customers are telling the truth,'' Sweetman said, adding that compliance with the strictures is helped by having nondrinking agents selling policies to people they know.

Asked whether this kind of specialty insurance will soon be offered by the major carriers, most insurance experts demurred.

''But I think it could be a growing area because of our national consciousness on driving while intoxicated,'' said Peter Strauss, vice president and regional manager of the Alliance of American Insurers, a trade association.