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There may be questions about the new Saudi king鈥檚 health, or about rivalries for power within the large Saudi royal family, or about the pace of reform in the kingdom.

But about the two issues that matter most to the United States when it comes to Saudi Arabia 鈥� oil price and production, and Arab participation in the battle against the Islamic State and Islamist extremism 鈥� the message from Riyadh is continuity.

And continuity, and stability, are two attributes that Washington will be looking for as the Saudi transition adds one more element of doubt to a region racked by turmoil. King Abdullah died early Friday and is being succeeded by King Salman.

Despite 鈥� or indeed perhaps because of 鈥� rising tensions in Saudi Arabia鈥檚 neighborhood, continuity and stability will be Saudi priorities as well, many regional analysts say. Those tensions include Yemen鈥檚 collapse into chaos, spreading Islamist extremism, and the rising influence of Iran.

鈥淚 see a lot of continuity going forward, and despite some disagreements between Washington and Riyadh that raised some questions for a while, the fundamentals of the relationship remain strong,鈥� says Frederic Wehrey, an expert in the Arab Gulf states and security issues at the Carnegie Endowment for International Peace in Washington.

One of those 鈥渄isagreements鈥� was over Syria policy, with differences between the two partners spilling into the open in September 2013 after President Obama called off airstrikes targeting Syrian president and Saudi enemy Bashar al-Assad.

But since then, relations have been patched up, Mr. Wehrey says, with the Saudis prominently joining the US-led coalition of countries bombing Islamic State positions in Syria and Iraq.

鈥淵es the Saudis were wringing their hands, and there were some theatrics,鈥� he notes, as when Saudi Arabia dramatically turned down a United Nations Security Council seat over what it said was the Council鈥檚 ineffectiveness on Syria. 鈥淏ut in the end, they鈥檝e realized there鈥檚 no one to replace Washington,鈥� Wehrey adds, 鈥渁nd so I think things are pretty much back on track.鈥�

The Saudis鈥� refusal to cut oil production to try to arrest the fall in oil prices has also been well received by the US, he says: 鈥淭he kingdom has done Obama a large favor by driving down the price of oil 鈥� and providing a boon to the US economy.鈥�

Another area of concern for Riyadh has been Mr. Obama鈥檚 extended hand to Tehran and progress in Iranian nuclear negotiations. But even there, the differences have been over strategies and have not pushed relations to a breaking point, other analysts say.

鈥淭ensions in the US-Saudi alliance have not focused on fundamental priorities,鈥� says Anthony Cordesman, a national security analyst and Saudi expert at the Center for Strategic and Studies in Washington.

鈥淭he issues have never been over the need to cooperate, they have been over how best to address the problems involved,鈥� Mr. Cordesman adds, writing on the CSIS website. 鈥淭here are no signs that anyone in the Saudi royal elite does not see the need for Saudi Arabia鈥檚 strategic partnership with the West to continue.鈥�

Conserving that 鈥渟trategic partnership with the West,鈥� and in particular with the US, has been a cornerstone of Saudi foreign policy since King Fahd in the early 1980s. Since then, Saudi Arabia 鈥渉as been run by a tightly knit group that sees the world in a remarkably similar way,鈥� Wehrey of Carnegie says.

That doesn鈥檛 mean there haven鈥檛 been sharp disagreements over those years. The Saudis opposed President George W. Bush鈥檚 invasion of Iraq, Cordesman points out, and the two countries differed intensely over Egypt, its revolution, and the return there of a repressive regime. Also, the US has on occasion questioned the lack of human rights inside the kingdom and the Saudi role in promoting Islamist radicalization around the region.

But Wehrey points to the evolution in US-Saudi relations over Syria 鈥� from what looked like an alarming split in 2013 to a gradually advancing convergence 鈥� as an example of how the two countries never allow things to get to the breaking point.

鈥淭he US has got more involved [in Syria] since then. The Saudis changed their point man on Syria鈥� and assumed a very public role in the US-led coalition against the Islamic State, he says. 鈥淓ach side moved back towards the other.鈥�

How to respond to the crisis in Yemen could be the next test for the US-Saudi alliance.

The Saudi government had already cut off aid to Yemen鈥檚 central government, before President Abdu Rabbu Mansour Hadi resigned Thursday, and in response to the virtual takeover of the capital, Sanaa, by rebel Houthis, a Shiite sect from the north of the country. Now reports are multiplying of the Saudis funneling assistance instead to Sunni tribesmen who are fighting the Houthis east of the capital.

But some experts like Wehrey say they would not rule out the Saudis coming around to some kind of accommodation with a Houthi government 鈥� especially following US overtures to the group. And if acknowledging the Houthis鈥� rise becomes the only way to head off Yemen falling under the influence of Iran 鈥� which has expressed support for the group 鈥� that, too, is likely to encourage the Saudis to swallow hard and follow the US lead.

鈥淥nce again we might get a sense of some strain in the relationship鈥� with the US over its tack on Yemen, Wehrey says. 鈥淏ut after some more of that hand-wringing, they might follow the US lead 鈥� especially if they conclude that the Houthis can be led away from Iran.鈥�