Banks accelerated their drive into mutual funds in the second quarter as assets under management grew to $354.1 billion, up 7% from the first quarter.

With the gain, banks captured 15% of the $2.35 trillion market for mutual funds. This compares with a 14.3% slice of a $2.3 trillion market in the first three months of 1995.

Mellon Bank Corp., PNC Bank Corp., and NationsBank Corp. continue to run the largest bank fund companies, according to a ranking compiled for American Banker by Lipper Analytical Services Inc., Summit, N.J.

BankAmerica Corp., boosted by a buildup of money market and equity funds, jumped over Wells Fargo & Co. and Banc One Corp. to snare the No. 4 spot.

BankAmerica's second-quarter asset growth allowed to bank to top the $10 billion mark that analysts believe is necessary for a fund complex to turn profits. Banc One also hit $10 billion, by adding $450 million of assets during the quarter.

A number of banks may have actually had somewhat higher assets at June 30, a Lipper analyst said. The company must sometimes wait a few months to receive information about new series or classes of shares.

By and large, there was little jostling among the entire pack of 118 fund complexes. All banks that were in the top 25 in the first quarter remain there, with some minor shifts of one or two positions.

In fact, only four of the bank fund families leapt more than five spots in the second quarter.

First Maryland Bancorp moved to 45 from 53, Meridian Bancorp went to 59 from 70, Trustmark Corp. climbed to 72 from 85, and Offitbank moved to 83 from 91.

Banks continued gaining ground as managers of long-term stock funds, after years of focusing almost exclusively on less fickle and less profitable money market funds. Equity assets grew 9%, to $82.2 million from $74 million, in the first quarter.

Assets in fixed-income funds grew 9%, to $35.5 billion from $33.7 billion, in the first quarter. Municipal bond funds also saw increases, though slight, with assets going to $31 billion from $30.7 billion.

Lawrence Kash, vice chairman of Dreyfus Corp., the fund giant that Mellon bought in August 1994, said the industry can expect investors to continue buying mutual funds of all stripes.

The markets are primed and interest rates remain relatively stable, two key components for continued growth, he said. "We're having a great year."

Dreyfus' already large asset base grew by $3 billion in the first quarter, largely through the national distribution juggernaut that Dreyfus established long before it was bought by Mellon.

Indeed, Dreyfus really shouldn't be grouped with bank fund families, Mr. Kash said.

"Dreyfus is not a bank proprietary fund," he said. "It's a large mutual fund company that happens to be owned by a bank."

While it's unlikely any of the bank funds will touch Dreyfus anytime soon, if ever, mergers will significantly change rankings among the other banks.

On the roster: Fleet Financial Group ($5.7 billion) and Shawmut National Corp. ($1.5 billion), PNC Bank Corp. ($24 billion) and Midlantic Corp. ($2.2 billion), NBD Bancorp ($6.4 billion) and First Chicago Corp. ($2.9 billion), and First Union Corp. ($9.2 billion) and First Fidelity Bancorp. ($2.7 billion).

"We're in a phase that will certainly be a factor in bulking up some funds," said A. Michael Lipper, president of Lipper Analytical Services.

Asset growth in bank-managed funds has come largely from mergers between banks, banks and fund companies, and from restructuring existing trust assets.

The strategic moves have given banks a cushion, but future asset growth may not come so easily.

Whether banks can actually sell funds - in branches and in trust departments - "is still not clear," Mr. Lipper said.

He questions whether investment units can wring out enough profit to avoid falling from favor with top management and seeing resources channeled to another part of the bank.

Indeed, while virtually all of the banks saw assets grow in the quarter, there were 15 bank fund complexes that slipped, declines that make profits that much harder to achieve.

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