China’s tightly controlled stock markets are loosening up amid great fanfare. ETF investors, however, are now beset with a new cluster of challenges.

As China has gradually allowed more foreign investment, more than $600 million has flowed into a young crop of US-traded ETFs that allow investors to buy and sell stocks that trade in Shanghai and Shenzhen-the total $1.4 trillion local-denominated A-share markets previously accessible only to heavyweight firms with special permission from the Chinese government. (Foreign investors were relegated to companies also listed in Hong Kong, where shares traded historically at a discount to A-shares from the same company.) About a half-dozen exchange-traded funds have launched or were modified over the past year to allow direct access to A-shares, via partnerships with Chinese asset managers. Most went into the $543 million Deutsche X-trackers Harvest CSI 300 China A-Shares ETF (ticker: ASHR), which has more than doubled in size this year; it has climbed 16% in 2014, while the iShares China Large-Cap ETF (FXI), which owns Hong Kong shares, is up 4% on the year.