Deputy Head and Senior Research Fellow, Middle East and North Africa Programme).
For the US, it was vitally important to avoid strikes against Islamic State (IS) looking like another Western attack on a Middle Eastern country, and to emphasize that opposition to IS comes from within the Arab and Muslim worlds - where the vast majority of their victims have come from.
But what's in it for the Arab countries?
The move reflects a combination of concerns about their domestic security and their international reputation. Longer term, beyond the concerns about IS itself, it reflects a desire on the part of these Arab states to play a more active role in regional security - but also illustrates the risks that can affect anyone wanting to become the policeman of the region.
Firstly, these states see IS as a threat to their own domestic security. IS's ideology doesn't only condemn the 'infidel West'; like Al-Qaeda (AQ), it is also dead set against the existing regimes in the Arab states, and wants the states themselves to fall and be replaced by a caliphate.
Saudi Arabia, which has confirmed its air force was involved in Tuesday's strikes, has been the victim of AQ attacks before, in 2003-04, and Jordan was bombed by an AQ affiliate led by Abu Musab al Zarqawi, an ideological precursor of IS. For its part, the UAE has accused the Muslim Brotherhood of plotting to overthrow it.
The UAE is the most hawkish of the five states when it comes to Islamists, and US officials say that UAE forces recently bombed Islamist militants in Libya, a claim dismissed by a UAE minister.
If so, this would be another indication of the growing military assertiveness of this small but wealthy country. However, if it happened it proved ineffective; the militants subsequently took Tripoli airport.
Second, for some Gulf states, especially Qatar, there is a worry that some in the West actually blame them for IS emerging. Several Gulf countries have been arming and funding a variety of Syrian opposition groups - as the West has too.
Gulf states say they've funded only 'moderate rebels', and that though this has included some Islamists, they are not IS.
But there are allegations of Qatari funding for Jabhat al Nusra, an Al-Qaeda affiliate, which Qatar denies.
Qatar is also being criticized harshly by Israel for supporting Hamas. For Qatar, therefore, a role in the airstrikes operation is a chance to counter the allegations that it supports terrorism.
It is also a chance to make a rare display of solidarity between Qatar and UAE, who have been at odds because they take opposing approaches to Islamists in the region.
Both the Qatari and UAE air forces participated in enforcing the no fly zone in Libya. But since then they've backed different sides in Libya. Indeed the Libyan PM has alleged that Qatari planes tried to take weapons to the militants holding Tripoli airport.
This evident disunity has weakened the foreign policy credibility of the Gulf Cooperation Council, the regional alliance of Gulf monarchies, so it has been especially important for the key Gulf players to pull together against IS.
The Saudi interior ministry has always been concerned that funding Islamists could lead to blowback. They've seen this before, with Afghanistan. However, it's less clear exactly what covert intelligence operations may have been supported in their bid to topple Assad and combat Iran; and when weapons and money go into a complex and fragmented civil war, it is not always certain where they will end up.
There has certainly been private funding from the Gulf; the UN has recently blacklisted several private individuals from the Gulf for funding ISIS and Jabhat al Nusra.
Several thousand Saudis have gone to fight in Syria - though with a range of opposition groups, some of which are supported by the West. And there have been claims in the Western media that the Saudi interpretation of Islam itself promotes this kind of exclusionary ideology - which Saudis reject strongly, saying their religion is against the shedding of innocent blood.
For Riyadh, this is a reminder of the period after 9/11, when US analysts seriously questioned the value of their alliance with Saudi Arabia. Indeed, as part of its response to IS, Saudi Arabia convened a regional counterterrorism summit on this year's anniversary of 9/11.
But for the Kingdom to take part in a US- led coalition is something much more dramatic, not seen since 1991, when Gulf forces joined US-led coalition to liberate Kuwait from Iraqi occupation. Saudi Arabian forces have been involved in fighting Houthi militants in Yemen in recent years, in a war almost entirely ignored by Western media. But both these conflicts were on their own borders, and had a defensive aspect.
Greater military assertiveness by the Gulf countries, and Gulf cooperation with the larger armies in Egypt and Jordan, are key regional trends to watch.
Gulf countries will remain keen to expand their own limited military capabilities and be less reliant on the US, just in case it is not always there to guard them.
Some in the Gulf, including the former emir of Qatar, have expressed frustration that the US was not doing enough to end the Syrian conflict and suggesting that there should be an Arab intervention.
However, until recently, they were talking about an Arab intervention against Assad. With this latest display of military force, the Syrians who sympathize with the opposition will be asking why these countries didn't have the same interest in defending them against regime attacks and chemical weapons.
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