One week after Saudi Arabia opened its stock market to direct foreign investment, U.S. mutual fund managers say they are interested but not rushing to invest in the Middle East's biggest economy.

Foreign fund inflows are slower than initially expected, in part because U.S. fund companies like Fidelity and Harding Loevner are digesting numerous regulations set forth by the Saudi Capital Market Authority (CMA) for participation in the $575 billion market.

"Investors are in the learn and plan stage, not the invest stage yet and the message is that the opening up is more of an evolution than a revolution," said Adam Kutas, manager of Fidelity's Emerging Europe, Middle East, Africa fund.

The investment stage, according to Kutas, will come in the next several months.

To buy shares, foreign investors must apply for a license from the CMA. Only institutions that manage $5 billion of assets and have a five-year record of investing outside the countries where they are based are allowed to participate.

No single foreign investor can own more than 5 percent of a company and overall foreign investment in a company cannot be more than 49 percent. Additionally, there is a 20 percent ceiling for all qualified foreign investors in any one stock and in total these holdings cannot exceed 10 percent of the whole market.

Until now, foreign investors have been restricted to buying shares in the market indirectly through swaps or exchange-traded funds.

"We are very interested, but we don't know the rules, so we are moving gradually because the process to become an investor is very vague," said Asha Mehta, lead portfolio manager for Acadian Asset Management's Acadian Emerging Markets Portfolio , which manages $70 billion in assets globally.

Pradipta Chakrabortty, lead manager of Harding Loevner's Frontier Emerging Markets Portfolio, is also interested in investing directly via the Saudi stock exchange, or Tadawul, but is still in the process of analyzing the various requirements.

Stock exchange chief Adel-al-Ghamdi told Reuters in Dubai that six applications from foreign investors for participation in the market are being processed, but only Ashmore Group and HSBC Holdings have been granted licenses so far.

Fund managers suggest tens of billions of dollars will eventually enter the country as a result of the opening.

"We see international appetite building up even if we don't expect this to translate into immediate on-the-ground investments in the short term," said John Sfakianakis, director of Middle East investing at Ashmore.