Eurozone services PMI slipped to 51.2 in November (flash 50.9) from 51.6 in October.
Composite PMI fell to 51.7 (flash 51.5) from 51.9.
Activity in Germany, Ireland and Spain grew, while it contracted in Italy and France.
The eurozone recovery "lost some momentum in November," says Markit. "It's clearly a concern that the rate of growth remains so fragile."
The survey indicates that the bloc's economy is on course to grow by just 0.2% in Q4.
The euro is -0.1% at $1.3578. (PR)