* Says rate of decline in energy demand slowing since April
* H1 operating profit falls 1 percent, beating forecasts
* Tweaks 2009 net profit outlook higher
* Shares rise 4.7 percent, outperforming market (Adds comments on energy demand, fund manager, Thuega sale)
By Peter Dinkloh
FRANKFURT, Aug 12 (Reuters) - Germany's E.ON, the world's largest utility, said it saw signs that demand for energy was stabilising after a prolonged slump, and tweaked its 2009 outlook higher after first-half profits beat forecasts.
The recession has cut power consumption rates, notably among industrial users, and several European utilities have said in recent weeks they expect the downtrend to continue.
But E.ON said on Wednesday it saw "the first signs that power demand contraction is abating, especially in North-West Europe," echoing a rare positive prediction from Spain's Iberdrola, which said last month it expected domestic usage rates to recover in the fourth quarter.
"E.ON seems to be benefiting from the strength of its industrial customer base," said Matthias Wilpert, who helps manage 62 billion euros at Commerzbank's Cominvest fund management unit.
The energy provider, Germany's second-largest company by market capitalisation, said better profits from domestic customers in the United States and higher margins at its pan-European energy trading unit also gave a boost to earnings.
It now sees full year net income falling 5-10 percent rather than 10 percent as interest payments and taxes will be lower than expected.
Shares in the nine-year-old utility rose 4.7 percent to 27.01 euros at 1221 GMT, the strongest riser on a DJ Stoxx utilities index that gained 1.6 percent and the German benchmark DAX, which was up 0.8 percent.
DOWNTURN TO CONTINUE?
Other large power firms in Europe, including Edison, are bracing investors for the downturn to continue. Italy's Enel has predicted the hard slog will last through next year.
Utilities remain pessimistic even though many -- including France's EDF, Enel and Britain's International Power -- have surprised investors with better-than-expected results.
E.ON's adjusted earnings before interest and taxes (EBIT) dropped 1 percent to 5.7 billion euros ($8.1 billion), beating a 5.5 billion euro average of estimates from 14 analysts in a Reuters poll. It said its still sees 2009 EBIT flat versus 2008.
PLAYING CATCH-UP
E.ON also said on Wednesday it had agreed to sell its Thuega unit, which groups minority stakes in German utilities, to a consortium of local firms for around 2.9 billion euros in cash, though Germany's antitrust watchdog said it expected the deal to be subject to an extended review.
Reuters had reported last week that E.ON was set to divest the unit.
The utility is trying to catch up with competitors as it struggles to earn money from 18 billion euros worth of acquisitions made in Italy, Spain and Russia, raise its profitability to the level of its peers and improve the performance of its shares.
Its stock has dropped 33 percent in the past 12 months, while the DJ Stoxx utilities fell 30 percent and the DAX 17 percent.
E.ON trades at 9.2 times estimated earnings per share for the coming 12 months, the seventh-lowest valuation among 33 European peers, according to Thomson Reuters StarMine, which weights analysts estimates according to their track record.
E.ON said on Monday its deputy chief executive, Johannes Teyssen, would take charge of the company from May 2010.
German peer RWE is due to report first-half earnings on Thursday and France's GDF Suez on Aug. 27.
(editing by John Stonestreet)