All of the reasons that make continuous integration a good idea are amplified by distributed development. Integration is a form of communication. Integrating distributed teams is just as important as integrating teams that are collocated. If you think of your teams as all being part of one giant collocated team, and organize in the same manner as described in the section on Multi-Stage Continuous Integration, it will be much easier to coordinate with your remote teams.
Getting to Multi-Stage CI takes time, but is well worth the investment. The first step is to implement Continuous Integration somewhere in your project. It really doesn't matter where. I recommend reading the book Continuous Integration by Paul Duvall, Steve Matyas, and Andrew Glover. The next step is to implement team or feature based CI. Once you have that working, consider automating the process. For instance, you can set things up such that once CI passes for a stage, it automatically merges the changes to the next level in the hierarchy. This keeps changes moving quickly and paves the way for easily adding additional development stages.
I've seen Multi-Stage Continuous Integration successfully implemented in many shops and every time the developers say something like: "I never realized how many problems were a result of doing mainline development until they disappeared."