China has instructed the Big Four auditors to hand over control of their Chinese operations to local partners by the end of the year and put a Chinese citizen at the top within three years, adding to challenges facing the companies in a fast-growing market.

China's Ministry of Finance said no more than 40% of partners at Ernst & Young, KPMG, Deloitte Touche Tohmatsu and PricewaterhouseCoopers can have gained their qualification as a certified public accountant from overseas. That number can't exceed 20% by the end of 2017, according to the guidelines, which took effect May 2 but were only announced Thursday.

The new rules, which will apply to both partners and managing partners, will given local partners a majority of votes in the new partnership the firms are forming, and effective control

Foreigners were brought in to help build China's accounting business more than 20 years ago, and the accounting giants may struggle to find enough local employees with the necessary experience to run their operations. By one estimate, more than 90% of senior positions are now held by non-Chinese.

The Finance Ministry's move may also complicate efforts to reassure investors that auditing problems of recent years, in which instances of fraud and misrepresentation went undetected, are under control. That could be particularly true if the new rules result in a forced pace of promotion for partners and if the experienced foreign employees necessary to help train the firms' rapidly expanding workforce are sent home.