Private equity firm Blackstone Group's chief executive said the worst of the industry's problems were behind it, and dealflow and IPO opportunities were opening up again.

Stephen Schwarzman also said on Wednesday he was seeing more than green shoots of economic recovery, though the scale of growth through next year was still unclear.

Private equity firms have been hampered since the credit crisis shut off their ability to tap financing for leveraged buyouts, and the financial turmoil has damaged the health of their portfolio companies. Economic recovery and a rebound in financing markets are key for the industry.

We do not expect the U.S. economy to slip back into recession but we do believe that weak consumer spending and continued constraints on bank lending will dampen the U.S. economic recovery in 2010 and 2011, Schwarzman said at the Super Return Middle East conference in Dubai.

While it would take several years before freely flowing but responsible credit was re-established, the private equity industry was in a radically different place than a year ago, given signs of life in the bank financing market, he said.

We can certainly do transactions in the $3-$4 billion range at this stage in the cycle, he said on the sidelines of the conference. And with low leverage involved, deals of that size can use in excess of $1 billion equity.

Blackstone, one of the world's biggest private equity firms, struck a deal earlier this month to buy Anheuser-Busch InBev's U.S. theme parks for up to $2.7 billion, adding to its amusement assets such as the Madame Tussauds wax museums, Legoland and the London Eye Ferris wheel.

Based on recent deals, Blackstone's implied annual investment rate is $4 billion to $5 billion a year, Schwarzman said.

He said right now is an excellent time to purchase stable businesses in developed markets, but added it was still too early for cyclical companies. He sees opportunities to buy growth companies in Asia.

Schwarzman said while he expects more deals ahead, Blackstone has been outbid by companies rather than private equity firms on several occasions recently.

EXIT STRATEGY

He said the route to exiting acquisitions had opened, citing five sales -- of which four are complete and one imminent. If all these sales are completed, Blackstone's funds will receive about $2.8 billion, he said.

In a letter to investors sent Friday, obtained by Reuters, Schwarzman said these sales occurred at prices between 140 percent and 240 percent of Blackstone's year-end 2008 valuations.

One recent exit is a deal struck in September to sell soft drinks maker Orangina Schweppes to Japanese brewer Suntory .

Schwarzman is evaluating the prospects for up to seven IPOs in addition to one -- Team Health -- already filed. The seven are spread across sectors and geographies, he said.

No one knows how long the window will be open for IPOs, he said. Historically its been a pretty streaky kind of market; and it responds well to the prospects for economic growth.

Blackstone has been managing on portfolio companies by reducing or extending $10 billion of debt on several companies through debt repurchases, debt-for-debt exchanges and extending senior debt maturities, Schwarzman said.

Schwarzman's letter detailed that only 7 percent of the debt in Blackstone's fifth buyout fund matures before 2013.

Schwarzman said Blackstone was open to investing in the Middle East and sees the firm opening an office somewhere in the region. He declined to specify where.

What historically has been the case is that there's been enormous financial resources in this area and... the investment opportunities have typically not outstripped the resources of the family groups and the institutions in the region -- so it's not been a robust area for conventional private equity.

(Editing by John Stonestreet, Dan Lalor and John Wallace)