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* STOXX 600 set for weekly loss

* Focus on ECB meet next week

* Computacenter surges after results

Sept 8 (Reuters) - Early gains in European stocks faded on Friday, with the benchmark STOXX 600 heading for its eighth consecutive session of losses as investors grew nervous over the trajectory of U.S. interest rates and the outlook for the European economy.

The pan-European STOXX 600 index fell 0.6%, putting it on course for its longest run of losses since November 2016.

Equity markets globally have come under pressure this week after upbeat U.S. economic data fuelled expectations of interest rates staying higher for longer, while weak data from Europe and China raised concerns about the health of the global economy.

"The economic data seen this week, especially from Germany and the rest of the euro area has been extremely disappointing," said Michael Hewson, chief market analyst at CMC Markets.

"It would take a brave central bank to hike rates further when economic activity is collapsing in one the biggest economies in Europe."

Despite the weak data, inflation concerns and hawkish remarks from the European Central Bank (ECB) policymakers have led money markets to increase their bets on a further rate hike in next week's policy decision.

Traders have priced in an around 40% chance of a 25-basis-point (bps) hike, up from 20% last week.

U.S. inflation numbers are also due next week ahead of the Federal Reserve's policy meeting later this month, with policymakers widely seen holding interest rates unchanged.

STMicroelectronics dipped 0.8% as a selloff in semiconductor stocks continued on worries about China imposing curbs on Apple's iPhones.

In the UK, stock of Round Hill Music Royalty Fund, which owns the copyrights to work of major artists such as the Beatles, soared 64% after a $496 million buyout offer from Alchemy Copyrights.

Computacenter jumped 6.5% after the IT service provider said its half-year adjusted profit before tax rose 8.8%. ($1 = 0.9339 euros) (Reporting by Sruthi Shankar in Bengaluru; Editing by Rashmi Aich and Janane Venkatraman)