Some suicide bomber teams do not rig their detonators to work until they are close to the target. They have good reason for this, for their have been accidental detonations, which kill the support staff as well as the suicide bomber. This is not good for the morale of the escorts, security detail and bomb technicians that make all the preparations for these attacks. THe bombers themselves only do it once, and are not as highly trained and difficult to replace. Without the support people, who are harder to recruit than suicide bombers, these attacks are not possible. When Israel began going after the support staff in the last two years, the Palestinian suicide attacks on Israel diminished, and there were more accidents from poorly made bombs, and more bombers were caught before they could reach their targets. TFB often brings along American and Iraqi troops to make a follow up sweep to grab as many of the support staff as possible.
TFB uses all available intelligence resources to find terrorist gangs that are making the suicide attacks. Most of them work for "al Qaeda in Iraq," but some are run by various Sunni Arab groups trying to get a civil war going between Sunni and Shia Arabs. The terrorists believe that such a conflict would result in a Sunni Arab victory. Realizing that an outcome like that is highly unlikely, some of the terrorist gangs are shutting down, and there has been a decline on terrorist attacks because of it. But the attacks continue, and TFB continues to have success in stopping some of the attacks, and killing or capturing support staff.
Such joint operations began in Afghanistan, in late 2001, where American and British commandoes worked together to hunt down Taliban leaders.
The United States often has its commandoes work together with foreign counterparts. One such instance is in Iraq, where Task Force Black (TFB) is composed of teams from the British SAS and the American Delta Force. The unit is used for difficult attacks on terrorists, especially if they are on their way to an operation (either on foot with explosive belts, or suicide car bombers.) These attacks are the most carefully planned and executed terrorist operations, and the objective of TFB is to take down the attackers before they can detonate their explosives. This is easier to do if you catch them before they are close to their target, because the bombers are not poised to set off their explosives on short notice.