* Saudi detentions could disrupt private sector activity
* But they may strengthen Prince Mohammed, speed reforms
* Several shares related to detainees get hit hard
* Falling stocks overwhelm gainers though banks strong
* Real estate stocks weak in Dubai
DUBAI, Nov 5 (Reuters) - Saudi Arabia's stock index rebounded to close higher on Sunday after initially falling steeply in response to a crackdown on corruption that led to the detention of dozens of prominent political and business figures.
A new anti-graft committee, headed by Crown Prince Mohammed bin Salman, detained 11 princes, four current ministers and tens of ex-ministers. Among them was Prince Alwaleed bin Talal, chairman of Kingdom Holding and, as a big investor in Western firms such as Citigroup, the country's most prominent international businessman.
By strengthening Prince Mohammed's authority, the crackdown could make it easier for him to push through economic reforms that investors want to see. Many foreign analysts, however, described the strategy as risky.
Raza Agha, regional chief economist at VTB Capital, said that by moving against many potential opponents since 2015, the ruling section of the royal family might be creating more enemies than friends.
"The alienation of the most powerful wings of the Saudi royal family and powerful private citizens, all of which have significant business interests, could create additional headwinds for growth via the non-oil economy."
Many local fund managers, however, saw positives in the crackdown. "It removes uncertainty over the royal succession and it's good for the economy because it tackles a problem that was ignored for too long," said one.
The Saudi stock index sank as much as 2.2 percent at one stage but recovered in the late afternoon to close 0.3 percent higher in active trade - with the help, one regional fund manager said, of government funds that deliberately intervened to support the market.
Declining stocks outnumbered advancing ones 126 to 49. Several shares linked to some of the detained people slid: Kingdom Holding plunged 7.6 percent and National Industrialization Co (Tasnee), in which Kingdom holds a 6.2 percent stake, fell 1.7 percent.
But the banking sector was strong with National Commercial Bank, the biggest lender, climbing 0.9 percent. Banque Saudi Fransi, in which Kingdom bought a 16.2 percent stake in September, added 1.0 percent.
Elsewhere in the Gulf, Dubai's stock index fell 1.0 percent as real estate-related shares dropped. Saudis are major investors in Dubai's real estate market and a big crackdown on corruption could conceivably affect investment by them.
The most heavily traded stock, Deyaar Development, lost 2.6 percent and blue chip Emaar Properties sank 1.4 percent.
Egypt's index lost 1.0 percent as real estate firm Talaat Mostafa pulled back 4.3 percent in heavy trade, after surging on Thursday on the back of strong quarterly earnings.
* The index rose 0.3 percent to 6,979 points.
* The index fell 1.0 percent to 3,586 points.
* The index dropped 0.3 percent to 4,451 points.
* The index fell 0.2 percent to 8,127 points.
* The index lost 1.0 percent to 14,184 points.
* The index slipped 1.2 percent to 6,468 points.
* The index dropped 0.4 percent to 1,278 points.
* The index rose 0.3 percent to 5,056 points. (Additional reporting by Davide Barbuscia; editing by Mark Heinrich)