Europe is the new battleground for the world’s largest hotel companies as they look for sources of growth outside the saturated US market.

Four Seasons Hotels, Starwood Hotels & Resorts Worldwide Inc. and Marriott International Inc. are stepping up expansion efforts in Europe, where about 34% of hotels fly chain flags, Otus & Co estimates. In the US, they already control about 70% of the market, according to Smith Travel Research of Hendersonville, Tennessee.

The chains can build market share in Europe by appealing to visitors from the US, China and India who are likely to seek out internationally recognized brands when traveling, said Rod Taylor, chairman and co-founder of hotel consultants Taylor Global Advisors Ltd. in London. Within the next five to 10 years, the branded chains may increase their market share in the region by 5 percentage points, according to Patrick Scholes, a New York-based analyst at Friedman Billings Ramsey & Co.