It is "probable, but not definite" that on-line brokerage trading volumes could decline for the first time ever in the third quarter, according to Credit Suisse First Boston Corp.

Though volumes rose slightly in July from June, they were "clearly" lower than April's levels, according to Bill Burnham, senior electronic commerce analyst at CS First Boston.

Mr. Burnham based his warning on an analysis of trading volumes in a group of Internet and high-tech stocks and on spot checks of the industry.

Recent weakness in the prices of Internet stocks, which have been popular with on-line investors, appears to be behind the expected decline in on-line trading volume, Mr. Burnham wrote in a research update. July share volumes in the group of stocks he tracks fell 54% from April.

Strength in these stocks in the first quarter had helped fuel record growth of 47% in the first quarter, Mr. Burnham wrote.

He said he does not expect a recovery in on-line volume until late September.

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