* Staffing, industrial, auto firms among those eyeing upturn
* U.S. companies also eye improvement
* Not all positive, some profit warnings hurt shares
FRANKFURT, Oct 27 (Reuters) - Down in the undergrowth of Europe's economy, something is stirring.
Whether they make paper to pack peaches, recruit temps for secretarial work or work at the dirty end, handling the waste that all businesses produce, managers are talking about signs the gloom is lifting and hopes that growth is on its way back.
The euro zone came out of a long recession in the second quarter and a survey last week of purchasing managers - a guide to how firms see their business growing in the coming months - seemed to confirm recovery, albeit tentatively, is taking root.
"There is certainly growing optimism that things are on the mend in Europe," said Vasant Prabhu, chief financial officer of Starwood Hotel and Resorts Worldwide, one of a host of executives to comment during the third-quarter earnings season.
The company, which runs Sheraton and other hotel brands, said it did well from tourists in Italy and Spain and made more revenue from each room thanks to a lack of new hotels opening.
Among multinationals whose job it is to fill the jobs that companies start to create as they expand, there is a similar sense of being at the leading edge of an upturn in fortunes:
"The positive signals that emerged during the previous quarter persisted in the third quarter," said Rob Zandbergen, chief executive of USG People, echoing comments from rival Manpower.
The staffing sector is seen as an economic barometer as firms tend to hire temporary staff first, waiting for further evidence of recovery before adding to their permanent payroll.
Zandbergen said companies dealing with logistics and making semi-finished goods - typically involved in the early stages of production before products reach their final buyers - were doing well: "A number of early-cyclical sectors returned to revenue growth in the third quarter," he said.
Another business close to the inner workings of industry, French waste and water company Suez Environnement, said the upswing had yet to arrive - but that at least things seemed to have flattened out after a period of decline.
"We are not seeing a recovery of industrial activity, but we are entering a phase of stabilisation," said Jean-Marc Boursier, finance chief for Suez, which sees a close correlation between industrial production and the volumes of waste it handles.
Companies that supply the construction sector, like France's Saint-Gobain and Britain's Travis Perkins, also appear to be early beneficiaries as housebuilding picks up.
Saint-Gobain, Europe's biggest supplier of building materials, which makes materials used in roofing and insulation as well as glass for windows and vehicle windshields, said market conditions were gradually stabilising in Europe and it expected a continuing rally in Britain and Germany.
Car makers said they finally saw some cause for hope after European car registrations steadied after seven quarters of decline - though their market remains difficult.
Ford Chief Financial Officer Bob Shanks said overall auto sales in Europe may see "very, very modest growth".
"The environment in Europe as well as industry sales may have turned a corner," he said. "We are feeling much more positive about that than where we have been the last year, year and a half."
Daimler Chief Financial Officer Bodo Uebber echoed that but cautioned: "Western Europe remains at a very low level and continues to be highly competitive."
Across the Atlantic, American companies are showing increasingly nuanced views on Europe, a far cry from the near panicked run for the exits of late 2011.
International Paper Co, for example, reported better-than-expected earnings, helped in part by a surprising improvement in European sales of industrial packaging. A better than expected harvest resulted in greater demand for boxes for avocados, peaches and other fruit and vegetables.
"The eurozone economy has hit the bottom," IP CEO John Faraci told Reuters in an interview. "As we look at our business there, the volume declines have stopped."
Dow Chemical, which has trimmed capacity in Europe and reported a 6-percent drop in quarterly sales volume, was nonetheless one of several companies offering guarded optimism about the next few quarters.
Rival DuPont also spoke of improvement and diversified manufacturer 3M reported its strongest quarter in Europe since the first three months of 2011.
"Conditions in Europe remain soft," said Dow Chief Executive Andrew Liveris. "However, in our view the market has found bottom and we expect to see more positive signals in the near term than in the previous three years, especially in the northern zone countries."
Translating early signs of future growth into profits will take time, however, not least for European companies who have seen a strong euro crimp the value of their overseas earnings.
A string of profit warnings hit European shares last week and an unexpected fall in the German Ifo business climate index on Friday cast doubt on the strength of the recovery.
According to Thomson Reuters StarMine data, 27 percent of the companies on the STOXX Europe 600 have announced recent results, of which 43 percent did not meet expectations.
Among them was French electrical gear maker Schneider Electric. CFO Emmanuel Babeau told Reuters: "Clearly Europe has remained extremely tough."