Flex equivalent of ProcessMessages and unresponsive UI during long loops?

The problem is that Flash is single threaded, i.e. Until a part of the code is running, no other processing can be made. You'll somehow need to break up the processing into smaller chunks and execute these chunks, say, on the enterFrame event.

I can tell you definitively that as of Flex 3, there is no built-in construct similar to the ProcessMessages functionality you are describing.

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