The Belzberg brothers, two Canadian investors, have been buying up shares in Bache Group Inc., a big Wall Street brokerage house, at a fast pace during the last month and now control nearly 20 percent of the company, New York sources said.

The Belzbergs themselves confirmed in a filing with the Securities and Exchange Commission that during late January and early February they bought nearly 224,000 shares of Bache, and sources said the brothers have bought more than 100,000 shares of the company during the last two days.

Their total share in the brokerage firm was nearly 2.04 million shares, about 18.9 percent of the outstanding stock, according to their Thursday filing with the SEC. But, with the purchases since the filing, the stake is above 19 percent, Wall Street sources said.

The Belzbergs, Samuel and Hyman, have been buying shares in Bache for more than a year, using their Vancouver-based financial services firm, First City Financial Corp. At first the Belzbergs said they had no interest in taking control of the brokerage firm but were purchasing shares merely as an investment.

However, in their SEC filing, the brothers indicated that, although they still are interested only in the investment, "depending on further developments," they may change their minds.

Bache officials said today that Samuel Belzberg, president of First City, last month asked for two seats on the Bache board of directors but was refused by the nominating committee. The nominating committee is composed of Bache Chairman Harry A. Jacobs, President H. Virgil Sherrill and three outside directors. The company would give no reason for rejecting Belzberg's request.

Bache has been wary of takeover attempts in the past and, in an attempt to prevent the Belzbergs from acquiring the company in 1979, convinced another set of brothers -- the infamous silver baron Hunts from Dallas -- to buy a "friendly" stake in the firm. The Hunts since have sold their holdings, some of them apparently to the Belzbergs.