Is the problem that it takes a long time to parse the XML, or is the problem that your code sits around waiting for e.g. HTTP requests to return?
It is possible to create nonblocking sockets in PHP, though things might get a tad complicated.It is possible to create nonblocking sockets in PHP, though things might get a tad complicated.
If you have expat installed, you can also set up event handlers to react to elements as they are parsed, which complements an asynchronous read very nicely.
Perhaps you can delegate this task to another process/service developed in a language that supports asynchronous operations. It won't guarantee a speedup (you still have to wait for both HTTP requests to return), but at least you can start working on data as they come in rather than wait until you've received all the data before starting to process.
Note that this is distinct from the second half of tdammers's answer. This answer focuses on keeping the retrieval and processing of the XML at "request time" (necessary when the data in the XML files change frequently and/or the data has to be "real time"), whereas tdammers's answer focuses on keeping the data in a cache (offers much better performance when the data don't change that often and/or if "stale" data are acceptable).