Bank stocks broke out of their six-day slump Tuesday, managing to post slender gains amid heavy trading.

Shaking off the swoon caused by the Asian financial crisis, shares of Chase Manhattan rose $1, to $103.625; BankAmerica Corp. was up $2.6875, to $65.3125; and Mellon Bank Corp. gained $2.3125, to $59.75, helping leading bank indexes to rise.

Though encouraged, market watchers were hesitant to say a corner had been turned. The gains were mostly small, and some high-profile banks continued to cede value. Fleet Financial Group lost 43.75 cents, to $68.9375, and Wells Fargo & Co. dipped $1.875, to $315.

The days immediately ahead are expected to help set the tone for 1998. "This will be a critical week," said veteran analyst Frank J. Barkocy of Josephthal & Co. The market is seeking "a catalyst to prime the performance of stocks again."

Overseas events and earnings reports will spur the drive-or the derailing-of bank shares, analysts said.

Illustrating their link with developments half a world away, bank shares, after falling last week in tandem with Asian markets, rose Tuesday after rallies by Hong Kong, Japan, and Singapore equity markets.

The banks' connection with Asian events is a little too close for the comfort of industry observers, who say bank stocks face a bumpy road as long as uncertainties exist in foreign markets.

"We're in a volatile, rollercoaster market where our bank sector is a prisoner of what goes on in Asia," said analyst George M. Salem of Gerard Klauer Mattison & Co.

Despite the pitfalls, banks have in their favor strong balance sheets, improving efficiency, consolidation, and solid earnings momentum, said Sean J. Ryan of Bear, Stearns & Co.

He said banks are poised to regain and far surpass the 10% decline the Standard & Poor's bank index experienced last week. On Tuesday the index was up 1.70%, and the Dow Jones industrial average rose 1.11%. The Nasdaq bank index gained 0.82%, and the S&P 500 increased by 1.37%

Gainers like Huntington Bancshares, up 50 cents, to $34.25, and KeyCorp, rising 62.5 cents, to $64.875, stood shoulder-to-shoulder with decliners like Regions Financial, down $1, to $38.125, and First Tennessee Corp., off 31.25 cents, to $59.9375.

So far, investors looking to earnings reports for indications of the market's direction are getting mixed signals.

Among the first banks to report, NationsBank Corp. offered encouraging indications by coming in with fourth-quarter results that met First Call's $1.12 per share consensus.

Still, the results were muted by management's statements about a slower pace for savings as a result of last week's purchase of Barnett Banks. Several analysts reduced 1998 earnings expectations as a result but maintained or even upgraded their rankings of the company. NationsBank closed unchanged, at $58.0625.

NationsBank has a top market share in six of the country's 10 fastest- growing markets, said Judah Kraushaar of Merrill Lynch & Co., who raised his recommendation to "accumulate" from "neutral."

Nancy A. Bush, associate research director and regional bank analyst at Brown Brothers, Harriman & Co., boosted her long-term ranking to "market perform" from "underperform," and her short-term ranking to "buy" from "hold."

"Lest you think we have softened on the NationsBank-Barnett deal, well, maybe just a little," Ms. Bush said in a note to clients.

She still maintains that NationsBank will experience difficulties with the integration of Barnett but feels better about management's taking less aggressive and less alienating steps as it melds operations with those of Barnett.

But Thomas K. Brown, perhaps the most outspoken critic of the merger, reiterated his "market perform" recommendation, saying the shares could reach $67 within a year.

He added, however, "it simply cannot happen" that NationsBank will achieve a 55% cut of Barnett's expense base without suffering a revenue loss.

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