* BASF Q3 adj EBIT 1.96 bln eur vs 1.89 bln forecast
* Solvay REBITDA 264 mln eur vs 261 mln forecast
* Bayer Q3 adj EBITDA 1.81 bln eur vs 1.66 bln forecast
* Tessenderlo opg profit 27.5 mln eur vs 22.7 mln expected
* Shares gain, buoyed by euro zone leaders' debt deal (Adds more details, background)
By Ludwig Burger and Aaron Gray-Block
FRANKFURT/AMSTERDAM, Oct 27 European chemical groups warned of slowing demand from construction industry customers in both fast-growing Asia and moribund Europe, compounding problems with rising raw materials costs.
The chemical sector's dependence on highly cyclical machinery makers, carmakers and builders makes it especially vulnerable to a downturn.
Germany's Bayer (BAYGn.DE) flagged a slowdown in China's robust construction sector, while global chemical industry leader BASF (BASFn.DE) said its construction chemicals business was unable to fully pass on higher raw material prices to customers.
"We see a certain weakness in Asia, mainly in China where the construction business is declining," Bayer Chief Executive Marijn Dekkers said, adding that this was weighing on demand for Bayer's insulation foams chemicals.
Bayer posted better-than-expected third-quarter earnings on Thursday, helped by cost cuts at its drugs unit and higher sales volumes of farming pesticides and confirmed its 2011 group outlook.
BASF, whose third-quarter earnings also beat forecasts, warned that growth was slowing as customers run down inventories.
"BASF's customers planned more cautiously, reduced inventories, and partially delayed orders in expectation of possible falling prices," the company said.
Belgium's Solvay , said a slowdown in global demand for PVC, used in construction "should be emphasised," adding the impact was stronger in Europe.
"Europe looks to be the worst of all. We have been fairly downbeat on growth prospects, if we can even talk about growth at all," said ING analyst Jan Hein de Vroe. "They all stick to their guidance, but these were never really challenging."
He said underlying results for the sector are worse than the headline consensus estimates and the companies are currently relying on cost cuts to protect earnings.
Solvay, which bought French rival Rhodia in September, said demand for vinyls and special chemicals has slowed, but stuck to its full-year outlook for improved core profit at its chemicals and plastic units.
Rhodia reported quarterly adjusted core earnings of 273 million euros ($377 million), up 16 percent from the year-ago period.
Bayer said its MaterialScience unit -- which makes the transparent plastic for the panoramic roof in the Mercedes SLK convertible -- would see a slip in operating profit this year, where it had previously seen stagnation, citing higher raw material and energy costs.
Shares in cyclical sectors, such as chemicals, on Thursday led a surge in European stocks after euro zone leaders agreed to boost the region's bailout fund and struck a deal with private banks and insurers to accept a 50 percent cut on Greek bonds.
That buoyed BASF and Bayer shares, up 6.4 percent and 4.9 percent, respectively, while Solvay rose 4.6 percent at 1151 GMT.
Belgian chemicals and plastics group Tessenderlo said its plastic pipes and window frames unit suffered a decline in profits, hit by low demand in construction. .
Its shares jumped 5.7 percent.
Dutch group AkzoNobel , the world's largest paints company, last week abandoned its 2011 profit outlook citing slowing economic growth and rising costs for some chemicals.
In contrast, U.S. chemical maker DuPont reported higher-than-expected quarterly profit earlier this week, boosted by price hikes for products such as pigments for paint. ($1 = 0.724 Euros) (Editing by Erica Billingham)