The recent record-breaking surge of money into stock mutual funds showed signs of tapering off in June.

But the funds still attracted a heavy inflow of money by historical standards, the Investment Company Institute reported Wednesday in its monthly estimate of industry trends.The ICI, the funds' largest trade group, estimated that investors put $15.5 billion more into stock funds in June than they withdrew.

That was down from an actual total of $25.16 billion in May, and represented the smallest monthly inflow so far this year. But it was also nearly double the inflow of $8.17 billion recorded in June of last year.

Industry officials said part of the drop-off was seasonal, reflecting the arrival of summer and the passing of the peak period for investing in individual retirement accounts and other tax-favored retirement savings programs.

They also noted that the stock market encountered some rough weather during the last month, with small stocks in particular giving up some of their gains from earlier in the year.

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John Rea, chief economist at the ICI, said the slowdown in cash flows occurred primarily in domestic stock funds, rather than international and world funds, but was spread about across all the major categories of funds investing in U.S. stocks.

Brian Mattes, a spokesman for the Vanguard Group, the nation's second-largest fund family, attributed the slower pace to both seasonal influences and the stock market's pullback.

Even with the June drop-off, net flows of cash into stock funds in the first half of 1996, at an estimated $138.5 billion, surpassed the record for any previous full year of $129.6 billion, set in 1993.

Flows into and out of bond funds were about equal in June.

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