$ tail -f log1.log log2.log | egrep “log1.log|log2.log|WARN|ERROR”

Another thing about tail (that’s often ignored) is that -f means to follow the file descriptor. The implications of this is that when the file roles over, you stop getting output, if you want to follow by name:

$ tail –follow=name alog.log

Or for some versions of tail:

$ tail -F alog.log