BEIJING (Reuters) - More Chinese cities are adopting stiffer measures on purchases of second homes, such as larger downpayments and tax requirements, as they scramble to dampen fast-rising prices.

Prices in many cities have risen by more than a fifth, as China's property market has roared back this year after a sluggish 2015.

The cities of Nanjing, Suzhou, and Hefei in the wealthy Yangtze Delta region around Shanghai are raising to 50 percent the downpayment required on a second home if the buyer already has another mortgage. The previous minimum was 40 percent.

In Suzhou, a new rule requires non-residents seeking to buy a second home in the city to have paid one year of local taxes and social insurance, the government said on Thursday in a notice on its website.

In Hefei, a downpayment of 40 percent is now required for any second home purchase, besides several conditions for loans to be issued, media reported on Thursday.

Data from the National Bureau of Statistics show July home prices rose 29.7 percent on the year in Nanjing, while the figure for Hefei was 29 percent.

Suzhou is not included in the official home price data, but private pricing data also shows strong gains.

First-tier cities Beijing, Shanghai, Guangzhou and Shenzhen have long-standing purchase restrictions, but as higher prices spread, more smaller cities are expected to clamp down.

(Reporting by Elias Glenn and Yawen Chen; Editing by Clarence Fernandez)