TOKYO (AP) _ A scandal over dubious dealings by Japan's ''Big Four'' brokerage houses brought down the presidents of two of the world's biggest securities firms Monday and increased calls for industry reform.

The scandal sent a ripple through stock markets, with prices falling sharply. One broker said the market was ''very weak'' early Tuesday, with the resignations still casting a shadow over trading.

Among those selling Tuesday were small investors incensed over the revelations that brokerage houses covered losses for their wealthy clients.

At the center of controversy is the practice of compensating wealthy clients, a cushion that smaller investors don't get.

News reports have alleged that the four houses failed to report millions in taxable transactions incurred in the course of paying the compensation.

Yoshihisa Tabuchi of Nomura Securities Co., the world's largest securities firm, and Takuya Iwasaki of Nikko Securities Co. resigned as presidents of their firms.

News reports also have accused those two companies of making millions of dollars of loans to an underworld figure and pushing up prices of a stock in which he invested.

The main index on Tokyo's stock exchange fell 2.1 percent Monday, and an additional 1.3 percent after opening Tuesday. One broker said the drop reflected disgust with brokerage practices.

U.S. stocks also reacted to the scandal. The Dow Jones average fell by 52 points, triggering the New York Stock Exchange's ''uptick rule'' that limited program trading by computers for the rest of the session.

Japan's business practices have attracted growing scrutiny in the United States, where an increasing number of leading Japanese corporations, from automakers to computer manufacturers, are establishing a significant presence.

On Wall Street, Tokyo securities giants like Nomura and Nikko have subsidiaries that trade securities and make investments like any other U.S. brokerage house.

Both Nomura and Nikko announced Monday that top executives would not receive their annual bonuses, which last year averaged nearly $83,000 for Nomura's top 40 executives.

Iwasaki bowed before reporters at a news conference, saying he hoped his resignation ''will be some apology to the society and industry.'' Tabuchi was teary-eyed as he announced his resignation at a separate news conference.

Iwasaki and Tabuchi both were named vice chairmen of their companies, leading some to wonder whether the companies were doing anything more than playing musical corporate chairs to improve their images.

''How will the people outside view the change in their status?'' asked the Asahi Shimbun in its Tuesday editorial. ''Will not the people on the street think that they were promoted from presidents to vice chairmen?''

In the past, such resignations have not necessarily ended careers or brought about change.

The Mainichi Shimbun said government heads should roll also. ''The responsibility of the Finance Ministry is great ... If the ministry remains unscarred, the government is too irresponsible and unfair,'' an editorial in the newspaper said.

Parliament has yet to consider election reform laws promised after a bribery scandal toppled the government of Noboru Takeshita in 1989. In fact, Takeshita is one of several tainted politicians who may soon return to prominence, perhaps winning his old job back.

On the Tokyo Stock Exchange, the average stock prices of Japanese brokerage houses fell 5 percent Monday, reflecting ''disgust that brokers are colluding with their best clients,'' said Mike Morizumi, an analyst with Lehman Brothers.

The drop in the Tokyo market affects some Americans who have mutual funds that invest overseas. In addition, many large U.S. institutional traders hold investments in the Japanese stock market.

For several days there have been media reports alleging that Nomura, Nikko, Daiwa Securities Co. and Yamaichi Securities Co. offered hundreds of millions of dollars in compensation to cover stock and bond losses.

The reports said the four houses failed to report a total of $143 million worth of taxable transactions incurred while paying the compensation.

The mass-circulation Asahi Shimbun also has reported that Nomura and Nikko arranged loans worth $258.9 million for Susumu Ishii, ex-leader of the Inagawa-kai underworld syndicate.

It said the two brokerages pushed up the price of shares in the railroad company Tokyu Corp. after Ishii made huge purchases of its stock.

The government has been trying to discourage securities companies from offering compensation to important clients, a preferential practice that critics say discourages smaller investors.

Two years ago, the Finance Ministry instructed securities companies to stop the practice in all circumstances, even though compensation is only considered illegal if it is offered to woo clients.

Nomura and Nikko have said they paid compensation but did not promise it to the clients.

Mitsuru Hasegawa, a spokesman for the Finance Ministry, said investigations were under way. He refused to comment further except to say that the ministry can penalize wrongdoing through admonitions, suspension of business licenses or cancellations of licenses.

''The series of incidents reported so far will undermine investors' confidence in the stock market,'' Finance Minister Ryutaro Hashimoto was quoted as saying by Kyodo News Service.

He said he hoped the disclosures would serve to clean up the two companies.

Alicia Ogawa, a senior analyst at S.G. Warburg and Co., said the outcry ''demonstrates that there's a kind of growing consciousness that some of the old rules are no longer acceptable.''

Peter Tasker, a strategist at Kleinwort Benson, said the scandals would boost the effort to crack down on questionable practices. But he added: ''You cannot change ... a culture overnight.''