* Services and composite PMIs at 8-month lows
* Service sector backlogs of work falls
* Firms hire fewer new workers in October than month before
By Jonathan Cable
LONDON, Nov 4 (Reuters) - Growth in the euro zone's dominant service sector slowed down last month, with Germany still in the fast lane but many smaller economies just chugging along, key private sector business surveys showed on Thursday.
The Markit Eurozone Services Purchasing Managers' Index (PMI), which monitors the performance of thousands of companies ranging from banks to hotels, fell in October to an eight-month low of 53.3 from 54.1 in September.
While that was revised up slightly from a flash estimate of 53.2 and still well above the 50 mark that divides growth and contraction, the survey showed activity was likely supported by a reduction in backlogs of work.
"The recovery also remains all too dependent upon France and Germany, and the steep slowing in the rate of expansion in France is therefore a concern," said Chris Williamson at Markit.
"Spain's problems seem to be escalating, with its service sector falling deeper back into recession."
Earlier data showed French service sector growth slowed dramatically last month and Italy's slowed as well.
But in Germany, Europe's biggest economy, the pace of growth accelerated on stronger client demand and improved conditions in the wider economy.
The euro zone composite PMI, a broader measure of private sector activity that combines both the services and the manufacturing PMI which on Tuesday showed a fall, slipped to an eight-month low in October of 53.8 from 54.1 in September.
The flash reading was slightly lower, at 53.4.
Survey compiler Markit said the composite PMI data suggested quarterly euro zone economic growth of 0.3 percent, down from 0.6 percent in the third quarter and a peak of 1 percent in the second quarter.
WORKING DOWN BACKLOGS
The report showed, however, that a significant contributor to growth in the past month came from working down existing orders rather than meeting new ones.
The service sector backlog of work index fell below 50 for the first time since the start of the year, down to 48.8 last month from 51.6 in September.
"The fact that this growth was partly achieved through backlogs of orders falling for the first time in nine months suggests that firms are struggling to maintain activity levels in the face of weakened inflows of new orders," Williamson said.
"If this continues, firms are likely to consider job cuts, meaning employment in the sector could soon start falling again."
The composite employment index fell further last month, slipping to 51.1 from September's 51.4, indicating firms were taking on new workers at the slowest pace since June.
Data released last week showed euro zone unemployment rose to 10.1 percent in September from a downwardly revised 10 percent in August despite a fall in the number of jobless in the euro zone's biggest economy Germany. (Editing by Hugh Lawson)