An American tourist in Italy is seen ransacking his raincoat pockets for his wallet in a television commercial.

"We have no money?" his wife asks incredulously. "We got problems," he sighs. Enter the announcer declaring American Express Travelers Cheques would have avoided the problem.

Yet American Express may soon have travelers check problems itself. Last week Visa, the leading credit card company in sales, announced it is challenging American Express, which has long held a monopoly in the travelers check business. Visa's announcement followed a formal statement six weeks earlier by Master Charge, its principal competition, that it too planned to get into travelers checks.

In recent years credit cards have enjoyed tremendous growth - there are now an estimated 712 million in use world wide - while travelers checks, which have been around for 86 years, have grown a modest 10 percent annually. In fact, according to Ernie Young, president of BA Cheque Corp., a subsidiary of BankAmerica Corp., the number of banks selling their own travelers checks have declined because there is too much risk and not enough profit involved.

So why are Visa and Master Charge now interested in travelers checks? For the same reasons Citicorp, Bank of America, Thomas Cook, Inc., Barclays Bank, Republic National Bank of Texas and other institutions are: market potential, increased services and diversified uses.

As a consequence, the travelers check war, like the credit card clash before it, is heating up - with resulting court battles, promotional blitzes and business infighting.

As in the case of the Visa-Master Charge dispute which wound up in the Supreme Court back in 1967, Citicorp already has taken legal action that seeks to stop Interbank, the organization of 9,600 banks that issue Master Charge credit cards, from issuing travelers checks. Interbank shot back with a countersuit charging Citicorp, issuer of First National City Bank travelers checks, with using terror tactics and even accused a Citibank vice president, who sits an Interbank's board, of being a double agent.

Meanwhile Cooks, the British owned travel agency, is planning to send letters to Interbank customers telling them Master Charge travelers checks are not a very good deal financially. Cooks has recently signed an agreement with Diners Club to sell members its travelers checks, while Citicorp has triumphed over an American Express court attempt aimed at preventing Citicorp from acquiring Carte Blanche, American Express primary card rival.

Last month a consortium of European banks, led by the Deutsche Bank of Frankfurt, announced development of a Euro Travelers Cheque. Barclays Bank has upgraded promotion of its free travelers check here by switching from spot to network television. Interbank has a $6.5 million ad budget for its proposed checks. American Express soon will begin issuing checks in a seventh currency.

American Express claims to have invented the type of travelers check currently used back in 1891. The spelling of "check" or "cheque" seems to be arbitrary, with more issuers leaning toward cheque, perhaps to distinguish the travelers instrument from the ordinary check or perhaps to make it more acceptable abroad by using the French word.

Interbank asserts it has been 40 years since the last successful issuer of travelers checks entered the market. There are no statistics on sales, but the domestic market is considered to be about $10 billion, the international market, $23 billion. Industry estimates generally give American Express a 60 percent share of that market, Citicorp 20, Bank of America 15, Thomas Cook 5, Barclays, Republic National and others 1 percent. When interviewed, each of the firms claimed a larger share.

One reason for Visa's entry into the field is what it deems an untapped market potential of many billions of dollars. Its studies found that travelers checks account for less than 10 percent of the $200 billion exchanged annually between buyers and sellers of travel and entertainment services. "We are primarily interested in the undeveloped market," said Visa President D.W. Hock. "However, we expect to capture a substantial share of the existing market."

He labeled American Express a "formidable competitor," but "vulnerable." Zane Sandom, vice president of Interbank's subsidiary, MCTC Corp., predicts that Master Charge Travelers Cheques will have a 19 percent share of the U.S. and Canadian market in a decade, most of it at the expense of American Express.

Competitors allege Visa decided to go into the travelers check business as a reaction to Interbank's decision. Indeed, Visa timed its traveled check debut to coincide with its announcement that it had just knocked Master Charge from its number one sales position. Both entries, it should be noted, are conditional; their success or failure will be determined by the number of participants each company manages to sign up. Sandom said Interbank would need to sign up banks doing a $1.5 billion annually in travelers check sales for its program to go forward.

Intense competition between credit card companies causes them to seek new gimmicks to entice Americans to add to the 5.2 cards the average consumer now carries. One method is packaged services. Credit card issuers are offering free safety deposit boxes, free checking, free travel insurance, or free travelers checks - often in exchange for a higher annual fee. Cooks recently made such a package arrangement with Diners Club and the American Automobile Association.

The ready access to mailing lists of millions of creditworthy individuals plus already existing worldwide communications networks needed to process credit transactions make offering travelers checks seem a logical extension. Yet BA Cheque Corp.'s Young contends that they appeal to a different clientele: customers who are used to paying cash in the form of currency or checks are not that apt to charge items, and vice versa. Interbank is betting it's not so.

Though companies don't like to talk about it openly, they are privately delighted at the increasing numbers of customers who use their checks not only for travel but as a form of savings and even speculation. There always have been people who for whatever reason keep a lot of cash on hand: travelers checks are viewed by some as a safer form of cash. Cooks alludes to the hoarding instinct in its advertising campaign claiming its checks are as "good as gold."

Both Cooks and American Express now sell their checks here in half a dozen currencies. Visa plans multi-currency checks too. Some investors have found buying yen or mark denominated checks allows them to hedge-against decreases in the dollar.

American Express invites its clients to keep a travelers check in their wallets for emergencies. Every day those checks go uncashed, the issuer makes a bigger profit on them by investing the funds until they must be paid out American Express had $1.86 billion in travelers checks outstanding last year up 8.3 percent over the previous year. According to Jack W. Cox, an economist and market analyst who follows American Express for the securities firm of Purcell, Graham & Co., the average life of a travelers check or float time is 40 to 50 days, and some have not been cashed for as long as 4 years.

The other way in which issuers of travelers checks make a profit is by charging the customer a commission commonly 1 percent in this area. How ever, in California and other parts of the country, par value (no commission) travelers checks are becoming the accepted custom. Agents such as banks who sell others' brand name travelers checks remit a fee to the issuer. American Express costs the agent the most money, 1/3 of the 1 percent commission, whereas Citibank and Bank of American each charge 1/10 of 1 percent; others like Cooks charge nothing. When a California agent is obliged for competitive reasons to sell American Express Travelers Cheques at par, he must still pay the company.

There is a natural tendency for the agent to sell the brand that nets him the most profit. Despite sales promotions like Citicorp's May offer where a $2 fee bought up to $5,000 in travelers checks and American Express' claim refunds for lost or stolen checks will be given at 60,000 places around the globe, studies show brand identification is a factor in only one sale in 10. The customer trusts the brand offered by his friendly bank, according to Scott Thomson, vice president of operations for Cooks; all he wants is "cashability."

Yet, he said, some banks are refusing to cash brands other the one they sell for persons other than their customers because the banks earn no profit on the check and are indeed out the money for the three to seven days it takes the issuer to pay them.

Visa Travelers Cheques, like the credit card of the same name, would be issued by individual banks, which assume the risks and liablities, while taking the profits minus a royalty and other fees. Master Charge Travelers Cheques will be issued by Interbank's subsidiary, MCTC Corp. Participants, who will underwrite the $20 million estimated start-up costs plus paying an annual fee and any other costs, get to keep the commissions and invest the proceeds.

This issue of a financial institution's ability ot favor one travelers check over another is at the heart of the suit Citicorp brought against the Interbank Card Association, a non-profit organization whose member banks in the United States share operating costs and revenues from credit card operations. Even before Interbank began inviting its members to issue travelers checks with the Master Charge logo, Citicorp (a large Interbank member) sued to stop MCTC Corp., on antitrust grounds. It charged MCTC would control the type or brand of travelers check purchased, resulting in diminished sales of Citicorp's own travelers check. American Express has concured in Citicorp's opinion. Bank of America says it welcomes the competition.

Interbank hit back in a countersuit alleging that Citicorp, the second largest private bank in the world, had used its suit as an in terrorem device to discourage potential members from signing up. Moreover, Interbank charged that David M. Phillips, a Citibank vice president who also sits on the board of Interbank, had violated his fiduciary duty to Interbank by circulating to the board copies of a letter from Citicorp's counsel that concluded MCTC would violate antitrust laws and might expose participants to antitrust suits and possible damages.