Data compiler IHS Markit said its purchasing managers' index (PMI) for services rose to 60.4 from 57.3 in October, the highest reading since May 2011. However, the figure was still well above the key level of 50: any figure below that suggests a contraction in the sector.
The Caixin China General Services Business Activity Index rose to 51.9 last month from 51.2 in October, marking the second month of acceleration and the highest reading since August.
Eurozone private sector growth strengthened in November, final data from IHS Markit showed Tuesday.
Duncan Brock, director of customer relationships at the Chartered Institute of Procurement & Supply (CIPS), said: "November's data painted a disappointing portrait of a sector struggling against Brexit-related uncertainty and a weaker economic outlook".
"Overall, the IHS Markit Russia Composite Output Index indicated a stronger increase across both manufacturing and service sector firms, with growth in the latest survey period at an eight-month peak", the analyst added.
"But we should be cautious because the economy may come under rising inflationary pressure at the start of next year due to continued price increases", Mr. Zhong said. Business activity climbed at one of the greatest extents seen over the past six-and-a-half years. The services sector is more labor-intensive than manufacturing, and policymakers are counting on it to create more jobs.