By Rex Crum, MarketWatch

SAN FRANCISCO (MarketWatch) -- Tech stocks began to show some signs of weakness Tuesday, even as sector bellwether Hewlett-Packard Co. rose following a pair of upbeat assessments from industry analysts.

H-P (HPQ) shares rose 2.3% to $27.34 after Citigroup analyst Jim Suva added the computer-industry giant to his U.S. Focus List. Suva said in a research note that there are many "positive catalysts" for H-P's stock, including a growing belief the company will beat quarterly earnings estimates next week.

Morgan Stanley analyst Katy Huberty also put out an upbeat research report on H-P, saying there are signs the company is set to benefit from improving demand in the U.S. corporate technology market.

Along with H-P, gains also came from Apple Inc. (AAPL), eBay Inc. (EBAY)., Pandora Media Inc. (P) and BlackBerry Ltd. (RIMM). See: Apple-heavy ETF primed for a potential breakout: analyst.

BlackBerry shares rose another 8% Tuesday, to $11.65, adding to Monday's gain of 10%. The company said Monday it's exploring various strategic options, include a possible sale.

However, the broad tech sector was in the red, with the tech-heavy Nasdaq Composite Index (RIXF) falling 11 points to 3,658.

Microsoft Corp. (MSFT) was among the decliners, down 1% at $32.33.

Brad Reback, an analyst with Stifel Nicolaus, cut his rating on Microsoft to hold from buy, saying in a research note that the company is facing headwinds in its Windows business that are "too much to ignore at current levels." Reback also took off his $36-a-share price target on Microsoft's stock.

Declines also came from Groupon Inc. (GRPN), which shed 2.7% to trade at $10.30, and Facebook Inc. (FB), off by 2.3% at $37.34.

Online travel agency Orbitz Worldwide Inc. (OWW) gave up 12% to fall to $10.34 a share. Orbitz said its largest shareholder, PAR Capital Management, sold 8.1 million of its Orbitz shares -- or about one-third of the 24.6 million shares PAR owned.

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