Editor's note: CNN's Barbara Starr is covering the Eager Lion military exercise in Jordan. Read all her reporting here.
By Barbara Starr
The tiny nation of Jordan may be one of the most important U.S. allies in the Middle East, but these days trouble is brewing from growing al Qaeda threats in the region.
In several days of talking here with senior U.S. military, diplomatic and Jordanian officials, the word most often heard is "instability." What worries Jordan is that regional stability could be shaken even more by unrest in neighboring Syria and also by Iran's nuclear intentions.
And the Syria and Iran problems increasingly may be linked.
These officials also informally believe that the Syrian crisis now essentially has distracted the Iranian leadership so much it may be lessening the immediacy of a nuclear weapons threat from Teheran. Up until a few months ago Jordanian leaders privately believed Israel was likely close to striking Iranian nuclear sites, but now they say, that seems to have eased.
But they also warn the Arab world sees the new Israeli government as a "war cabinet," and Iran could make the decision yet to proceed with a nuclear agenda.
Still, the worries Jordan feels from Iran are significant.
"Iran is a problem for the whole region," one official here said. Hezbollah ties to the Islamic Revolution Guards Corps (IRGC) are now virtually complete, Jordan feels, with the Iranian regime providing the group weapons and full financial and other support.
Jordan is in fact worried Hezbollah operations could target it.
The most senior Jordanian officials tell CNN they do not believe Syria's president, Bashar al-Assad, has any intention of attacking Jordan, knowing that would bring down the wrath of the United States.
But the Jordanians' worry is more complex.
Jordanian officials say there is extensive evidence Iran's Revolutionary Guard Corps is shipping weapons to the Syrian regime and that Russia is determined to keep supporting al-Assad, so that it has a base for intelligence operations. Those weapons are mainly limited to hand-held weapons such as AK-47s that Syrian troops can use in urban assaults.
In addition, Jordan now believes there are upwards of 1,500 al Qaeda operatives and sympathizers in Syria, most coming in from Iraq. U.S. intelligence officials tell CNN's Suzanne Kelly that the U.S. believes there are approximately 500 al Qaeda operatives in Syria but cannot quantify how many more sympathizers there might be.
In recent weeks there have also been infiltrations from Lebanon, and trouble has erupted on that border.
Jordan's own long northern border with Syria remains stable, for now. But officials say they have caught smugglers, and even a small number of people trying to bring weapons into Jordan. They've also caught Syrian intelligence agents coming into Jordan to spy of the growing Syrian refugee population.
All of that equals worry.
The Jordanian military also has stepped up its training with U.S. special forces, just in case.
"We have to anticipate any surprises," from Syria, says a senior Jordanian official. Elite Jordanian special forces and U.S. Army Green Berets are training in Jordan in case they have to move to secure Syria's chemical or biological weapons. There is even on-going training on how to rescue a downed pilot.
Jordan already is struggling under the economic burden of tens of thousands of Syrians refugees. If al-Assad pushes more out of Syria, that, too, could destablize Jordan's already shaky economy.
But for the United States, the most direct worry still comes from al Quaeda in Yemen, also known as al Qaeda in the Arabian Peninsula (AQAP). The Jordanian assessment is that some Jordanian fighters have traveled to Yemen to join the group as well as fighters from the Palestinian territory, Iraq, Saudi Arabia, Kuwait, the UAE and Libya