WASHINGTON — (CNN) U.S. President Barack Obama is sending Special Forces. British jets have joined French warplanes over the skies of Syria. Even Germany, whose post-World War II constitution puts restrictions on fighting battles on foreign soil, is becoming increasingly involved.

But as the West steps up its war against ISIS, it appears that the involvement of the U.S.-led coalition’s Arab members — all of them much closer geographically to the terror group than their Western partners — is drawing down.

Saudi Arabia and the United Arab Emirates are down to about one mission against ISIS targets each month, a U.S. official told CNN on Monday. Bahrain stopped in the autumn, the official says, and Jordan stopped in August. CNN contacted all of these countries for comment and is yet to receive a response.

Why aren’t Arab countries more involved in the fight against ISIS?

Yemen — not ISIS — is the priority for most Arab countries

Analysts say Yemen is at the center of a proxy war between Saudi Arabia and Iran, the region’s biggest powers.

Religion and ethnicity are at the heart of the longstanding hostility between the two countries. Iran is majority Shia Muslim and non-Arab. Most of the other countries in the region — including, and led by, Saudi Arabia — are majority Sunni Arab, and are suspicious of Iran’s motives.

So when Iranian-backed rebels seized Sana’a, the Yemeni capital, last year, a Saudi-led coalition of Arab states (including Egypt, Jordan and the UAE) was launched to try to defeat them.

“The critical shift was the coalition in Yemen,” says Fawaz Gerges, a professor of Middle Eastern Studies at the London School of Economics. “You’re talking about a major 24/7 war. The Saudis and the Emiratis — the two countries with the most capacity in terms of air power — are flying fighter jets over the skies of Yemen, so that’s why you really have to prioritize the fight in Yemen over the fight against ISIS.”

They’re worried about what will happen at home

Yemen may have distracted many Arab states, but the threat of opposition — not to mention revenge terror attacks — at home has also made them fearful of greater involvement in the ISIS fight, according to analysts.

“The Arab states, including Jordan — after the incident with the pilot [burned to death by ISIS when his plane crashed in Syria] — are laying low,” Gerges says. “ISIS doesn’t just exist in Syria and Iraq — it has major constituency supporters in almost all Arab countries, including Saudi, Kuwait, Lebanon and Jordan. So they want to really minimize the risks.”

“Also, remember that one of the largest contingencies within ISIS are the Saudis. They’re not just fighters, they play leadership roles — and ISIS has carried out major attacks in Saudi, both against Shiite mosques and against (other) Saudi targets.”

Arab states have long seen ISIS as Iran’s problem, not theirs

The governments under the most immediate threat from ISIS — those of Syria and Iraq — are both key Iranian allies, so why can’t the Iranians handle it?

That’s been the prevailing logic amongst the Sunni Arab states, according to regional experts. They say Saudi Arabia and its Gulf allies are also less inclined to carry out strikes against ISIS targets if doing so helps Iran’s allies in Damascus and Baghdad.

But Gerges says that view is evolving now that ISIS has grown into a global network claiming terror attacks from Paris to Australia. “There’s been the idea that ISIS is a bigger challenge for Iran and its allies than it is for the Arab states, even though this feeling is changing now.”

“ISIS has threatened not only Iran and the [Shia]-dominated regimes in Iraq and Syria but even the Sunni-dominated Arab states.”

The problem with deploying a large number of Arab troops is that no individual country is likely to risk it, and no nation has a mandate to act on behalf of everyone else.

Even if that wasn’t the case, the likelihood of Syria or Iraq endorsing foreign military intervention is extremely unlikely, according to Ghadi Sary, a Middle East expert at Chatham House.

“I think it’s going to be very hard for that to happen — you’ve seen the Iraqi reaction to the presence of the Turkish army in northern Iraq,” Sary says, referring to Iraq’s ordering of Turkish troops out of the country on Monday.

“It is important for any intervening army to have the backing of the central government, or at least the army in the country,” Sary says, “(including) the army of Syrian President Bashar al-Assad, who everyone will see as impossible to work with.”

Sary also says most Arab militaries are more comfortable working inside — not outside — their own borders.

“For most of these countries, the over-involvement by the army in the internal affairs of the state has become acceptable, but when it comes to foreign intervention, it becomes problematic,” he says.

“We’re seeing the Egyptian army focus on the Sinai and its internal problems, we’re seeing the Syrian army doing that, and in Yemen it’s almost seen as the Saudi army cleaning up their own backyard — but not really intervention on the international level.”

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