Officials of the Tokyo Stock Exchange, the second largest in the world, were undecided over which of 10 securities firms to admit as its first foreign members as the deadline for applications passed last week.

The deliberations mark one of the most important openings of Japan's vast financial markets in recent years and result to a large degree from pressure from the United States.

The Tokyo exchange is currently an exclusive club of 83 Japanese firms, ruled over by the Big Four -- Nomura Securities Co., Yamaichi Securities Co., Daiwa Securities Co. and Nikko Securities Co. -- which handle about three-quarters of all trading in a market where sales can exceed $1 billion on an active day. Only New York is larger.

Starting in January, the club will get 10 new members. It has made no public promises as to how many will be foreign, but expectations in securities offices here are that four, five or six will be. The decision is due in late November.

"We are so busy preparing for future expansion," said Yasuji Aramoni, chief financial officer at the Tokyo branch of Merrill Lynch Securities Co. It has led the fight for foreign membership and the affiliated Merrill Lynch International Banking Corp., one of the 10 applicants, is regarded as a shoo-in . . . . We will be encountering a field we've never encountered before in Japan," he said.

The other foreign applicants are: Goldman Sachs International Corp.; Morgan Stanley International Ltd.; Salomon Bros. Asia Ltd.; First Boston (Asia) Ltd.; Smith Barney, Harris Upham, International Inc.; Vickers da Costa Ltd., all of which are U.S.-owned; S. G. Warburg, Rowe & Pitman, Akroyd (Japan) Inc., and W. I. Carr, Sons & Co. (Overseas) Ltd., which are British affiliates; and the Hong Kong firm Jardine Fleming Holdings Ltd. All already have branches in Japan.

In addition, eight Japanese firms applied.

Those accepted will have to pay up-front membership fees of between $4.8 million and $5.2 million, depending on capitalization and other financial indicators, for the privilege of having their own people on the exchange floor.

The price is steep, and for most companies, profits will come slowly, if ever. But it has become a matter of commitment to the Japanese market and credibility. "You don't know if they'll ever open up again," said an executive at a U.S. firm here, who added that even a higher entrance fee wouldn't have deterred applicants.

The 10 applicants now can trade on the exchange by placing orders through Japanese firms, and get a 77 percent discount on the brokerage fees they pay.

However, many feel the system has locked them into being fringe players in the world's second-busiest market. The pounding on the doors grew louder as the Japanese got seats on U.S. and other foreign exchanges. (Three of the Big Four now have seats in New York.)

Several years ago, the exchange formally rewrote its rules to permit foreign members, but no seats were available. In New York, seats go to individuals and are bought and sold routinely; in Tokyo, they go to companies and almost never change hands.

A breakthrough came in an accord signed by the United States and Japan in May 1984 for long-term liberalization of the financial markets here. In it, Japan pledged to look for ways to open the exchange. Suddenly, executives there began feeling heat from the powerful Ministry of Finance.

While the search was on last year, a rare opening was created when Yamaichi merged several of its affiliates. Merrill Lynch bid for it, but lost out to a Yamaichi affiliate based in Hiroshima.

But last month, the exchange finally came up with a long-term solution: 10 new seats, a number that officials say is the maximum possible because of the limited floor space in the stately granite building the exchange opened earlier this year.

The selections are being made in near total secrecy (by some accounts, in fact, they already have been made). Applicants have been required to submit financial data and background on their history in Japan, but have not been told by which criteria membership will be awarded and will have no formal rights to appeal.

Japanese officials maintain there is no standard yardstick by which to measure securities houses and that the decision only can be done this way. So far, the foreigners do not appear to have raised serious objections, even though the United States has been pushing Japan to lift the veil of secrecy that often covers the decision-making process in government bureaucracies.

Unofficial lobbying is underway, however. Some companies such as Salomon Brothers have flown their chairmen out to pay courtesy calls at key offices around town and to underline their interest.

Foreign pressure was the trigger for the opening but, by many accounts, the bigger firms in the Japanese industry have slowly warmed to the idea on their own.

The Big Four, with plans for major new operations in New York, London and other world financial centers, have met resistance from regulators there who want reciprocal access to the Japanese market.

Japanese firms will lose brokerage fees they now collect from the firms that are to become members. But there still will be major business from the foreigners in the form of research and other services.

Nor is there reason to expect that foreign members will monopolize orders from foreign investors, which account for about 10 percent of all exchange transactions. With the Big Four set up in foreign centers, they will rope in much of that business before it gets to Japan. In addition, they will be the only ones capable of settling some of the big orders.

A foreign member with an order for 10 million shares of Nippon Steel, for example, would have little choice but to call on a Big Four company, said Jean-Pierre Sevos, first vice president of Painewebber International. "They could go to one of their subsidiaries and say, 'you have 200 million shares of Nippon Steel and would you mind selling 10 million?' " he noted.

The major Japanese companies hope the presence of foreign firms will convince more foreign companies to list here (there are now 18) and bring in more foreign capital and new ideas. More people will be feeding on the pie, conceded Kiyoshi Asakawa, a deputy director general at Nikko. "But the pie itself will be bigger," he noted.

What apprehensions exist are found more in smaller companies. They have nothing to gain from added access for Japanese overseas. They also fear that foreign members could disrupt their traditional relationships with big firms and lead to dangerous ideas such as dropping the exchange's fixed-brokerage-fee system.

Two foreign firms that are active already in Tokyo, Kidder Peabody & Co. and Bache Securities (Japan) Ltd., an affiliate of Prudential-Bache Securities Inc., have elected not to apply. "We feel the Japanese market has a good future," said Bache Executive Vice President Hisamichi Sawa. "But we wonder if it is possible to be profitable after paying the membership fees."

For those who remain outside, there is talk of eventual access through the creation of some type of less-expensive associate membership, or indirectly through the advent of 24-hour trading. Any such changes, however, are likely to come very slowly.