Despite their reputation and history of aiding and abetting terrorist groups, the Syrians are becoming increasingly nervous about the large numbers of al Qaeda terrorists that have crossed their border into Iraq. At the height of the fighting (2005-6), before the U.S. troop surge, the vast majority of terrorists entering Iraq came through Syrian. Most of the fighters were, and aren't, ethnic Syrians, but instead come from Saudi Arabia and North Africa. The reason for all this lies in Syria's geographic location and porous, corrupt border.
With the troop surge having pushed al Qaeda out of their previously invulnerable strongholds in Iraq, more and more foreign fighters are quitting the Iraq fight, seeing it as a lost cause. Increased pressure on the Syrian border movements of terrorists, has also strangled most of the smuggling routes used to transport cash, men, and weapons into Iraq. While the US has a hand in stopping the smuggling, the Syrians and the tribal smugglers have also contributed to cracking down on the terrorist networks.
Unlike Iran, which actively supports Iraqi terrorists with cash and training, the Syrians are far more reluctant to help. Meanwhile, Syria aids groups like Hamas and other Palestinians groups more enthusiastically. This is because Hamas and Syria have an active common enemy with which they are at war; Israel. By giving their support, the Syrians can make life difficult for the Israel without actually engaging in a conventional conflict, which they would lose in an embarrassing fashion. Secondly, groups like Hamas concentrate almost single-mindedly on destroying Israel and reclaiming Palestine for Islam, which means they are less interested in fighting the U.S. or other secular Arab states. With a common enemy to preoccupy them, all parties involved cooperate.
Al Qaeda's Iraq fighters, however, are a different matter entirely. Although active against the Iraqi Security Forces and coalition troops, Syria is well aware that groups like al Qaeda are frequently just as dangerous to secular Muslim countries as they are to infidels (non-Moslems). Syria, although Moslem, is officially a secular nation and has become increasingly corrupt, incompetent, and autocratic over the last 30 years. All these factors are fertile ground for Islamic terrorism and uprising, which groups like al Qaeda specialize in exploiting to gain more recruits and support. The Syrians realize all this could be a major problem in the future.
Al Qaeda, of course, considers Israel an enemy, but it's much easier for terrorists to operate and strike in countries with popular domestic discontent, corrupt officials, and secular governments. In other words, countries like Syria.