Consumer marketers long have offered free trials of everything from soap to encyclopedias in the hope that customers will try a new product, then like it well enough to buy it.

Banks here and nationwide are using a similar strategy to sell consumers on the convenience of automatic teller networks -- the web of computerized banking machines that enable patrons to get cash and check balances on units in grocery stores, shopping centers and other public places.

Teller machines have gained widespread use in the last five years among financial institutions, which believe that machines will prove less expensive to employ than flesh-and-blood workers. To encourage use of the electronic banking service, most banks have offered it without charge.

Networks of machines owned by different banks, or even outside investors, have become particularly popular because they enlarge a bank's electronic service area without requiring the purchase of additional machines. But as banks expand their reach through networks that link them to the terminals of competing banks, more and more have decided to charge for the added service. They reason that customers have had a free taste of self-service banking long enough and are ready to pay for new versions of it.

Not everyone agrees. "How can anyone justify charging customers a fee for using automatic tellers? That's crazy," said John Love, publisher of Bank Network News, an industry newsletter in Chicago. "The whole point of shared delivery is to reduce costs. It's cheaper for a bank to send a customer across the street than to install a new machine. Charging is nuts."

Of area banks that belong to an automatic teller network, an estimated 40 percent give customers free use of networks, making no distinction between their own and others' terminals. But the larger, growing group of 60 percent think consumers are ready to pay for the ability to get cash and check balances on almost any teller machine they see.

American Security, for example, the second-largest bank in the District, on Feb. 1 began charging customers 50 cents each time they use a competitor's machine. It will continue to offer its customers free use of the terminals it owns. National Bank of Washington, which joined a network in 1982, adopted a similar fee policy early last year.

These banks, which say they merely are passing on the charge competitors assess them for use of the machines, are betting that fees won't dampen use of automatic tellers. After all, they say, many banks here and in Texas and Florida have charged for the use of competitors' machines for months, or even years, with little, if any, drop in volume.

But institutions such as Riggs National Bank, the largest bank in the District, and NS&T, which soon will merge with United Virginia Bankshares, aren't so sure. These banks concede that electronic-banking fees will become standard, but nevertheless have decided that they won't charge in the near future for any kind of automatic-teller transaction.

They worry that customers aren't ready for such costs and that fees could retard electronic banking. The public has thus far accepted it less quickly than bankers would like -- only one of every three people who could use self-service machines does.

The question now is whether fees will change those numbers. Until the answer is clear, Riggs and other banks say they will use prevailing uncertainty to their advantage by using lower prices to distinguish their products from the nearly identical services of competitors. "Charging for electronic banking is the trend," said one Riggs executive. "We're just not sure now is the time to do it." Nationwide Debate Continues

The difference of opinion among local institutions over automatic-teller fees is part of a debate among bankers nationwide as they search for ways to supplement shrinking interest-rate spreads. Spreads are the difference between the money a bank pays out on deposits and the money it takes in on loans.

Advances in technology and deregulation of interest rates during the last five years have torn down the legal and geographic boundaries of banking, blurring distinctions among financial industries and introducing an unprecedented level of competition in the industry.

As a result, bankers have been forced to use pricing to distinguish an increasingly similar array of products. As depositors demand higher interest rates and businesses demand cheaper loans, banks have started to nickel-and-dime the public whenever possible to make up for shrinking profit margins.

"Banks are searching for fee income where they can find it. Automatic-teller charges are a small piece of a larger pie," said Joseph B. Head, a senior vice president at D.C. National Bank, which has charged a fee for use of its own and competitors' machines ever since it installed its first and only automatic teller 18 months ago.

Said Steve Demaree, research manager of retail banking services at the Bank Administration Institute, a nonprofit think tank funded by the banking industry, "Financial institutions always knew that charging for electronic services would be inevitable." But bankers also knew that to accept such charges, "customers would first have to perceive the value of a product. That's why there were few fees in the early 1980s," he said.

Banks such as American Security counter that after years of exposure to teller terminals, customers who use them will continue to use them, fee or no fee, and similarly, those who avoid the machines will continue to resist, but for reasons other than price. Others, however, say market research so far hasn't supported or disproved such conclusions.

Automatic-teller-machine networks usually are run by for-profit companies that use computers and telephone lines to link teller machines owned by different banks, thus allowing customers of one institution to use the equipment of another.

When a bank customer uses a competitor's machine to get cash or make a balance inquiry, the bank pays a fee to the network-exchange company. A bank pays the network nothing for transactions by its own customers on its own machines.

The Washington area's largest network, Most, has 147 members, half of them banks in the District, Maryland and Virginia. It charges 55 cents each time it links terminals of competitors, from which it keeps 15 cents and gives 40 cents to the bank that owns the machine that was used.

At issue now is how such costs will be passed to consumers. Since Congress began lifting the lid on interest-rate ceilings in 1980, the public has watched fees for checking, credit cards and other bank services skyrocket. A study by Sheshunoff & Co., a banking research firm in Austin, Tex., for example, found that the average fee for bouncing a check nearly doubled between 1980 and 1985, while the average monthly maintenance fee for a checking account more than doubled during the same period.

"Price is a marketing issue, that's clearly the case," said Michael F. Ryan, president of NS&T Bankshares and president of the D.C Bankers Association. "The big issue of the future is service delivery -- how are we going to get the product in front of the customer and get them to use it? Pricing will play a big role."

But pricing is an incentive pro and con, he said, "and we bankers are our own worst enemy." He cited industry fears that deregulation will spark deadly price wars like those that have undermined the financial stability of the airline industry since it was deregulated in 1979.

Other bankers prefer to think that they will be able to use two-tier pricing -- the way telephone and oil companies have -- to induce consumers to dial their own calls and pump their own gas. Those practices have saved millions of dollars each year in reduced costs for operators and station attendants.

Getting consumers hooked to self-service banking could produce similar savings for the financial industry. ATMs Cost $50,000 Yearly

According to some estimates, the average machine costs about $50,000 a year to operate, while the average human bank teller costs about $18,000 in salary, plus benefits and overhead. Because machines work 24 hours a day and the costs associated with them vary less than the costs of human tellers, electronic banking becomes cheaper the more it is used.

Although a teller handling lots of transactions could prove more cost-effective than a machine with low volume, most industry executives say that, in the long run, self-service banking will prove cheaper. Even so, they say, machines cost money to run, and it is only a matter of time before consumers are charged for each electronic service they use.

At least three area banks have been using innovative pricing policies to encourage use of banking machines.

Suburban Bank in Bethesda charges customers with regular checking accounts 60 cents to make a withdrawal from a competitor's machine. But it also offers a checking account that charges 25 cents per check, but only 15 cents per automatic-teller transaction. Though aimed at people who write few checks each month and don't want to maintain the minimum balances required to waive monthly service fees, such accounts reflect "a first step" in providing a price incentive to use computer terminals whenever possible.

Maryland National in Baltimore also charges for using competitors' machines, but it ties fees for checks and use of its own teller machines to account balances. And for certain accounts, it charges 35 cents for each check, but only 20 cents for use of the teller machine.

Payment Systems Inc., a banking research firm in Tampa, Fla., said that as networks flourished in the last two years, bigger banks owning more machines thought they would get extra income from fees charged when competitors' customers used their machines. Instead, many have found such setups a cash drain, especially in areas such as Washington, where many people live and work in different banking districts.

For such reasons, few banking experts challenge the assumption that, in the long run, customers are going to see fees attached to more and more services and see existing fees hiked, according to Demaree of the Bank Administration Institute.

American Security, for example, said that 30 percent of its ATM transactions are made on competitors' machines. "The sharing arrangement makes it more convenient for customers. If the fee makes a customer more likely to use our machines, then, frankly, we think that's fine," said Roger Conner, a bank spokesman.