ps axu|grep grep doesn't output always

[Dan Jacobson <jidanni@jidanni.org>]

Just curious, why doesn't this make output every run:
$ ps axu|grep grep
jidanni   1163  0.0  0.2  2376  608 pts/1    R    02:26   0:00 grep grep
$ ps axu|grep grep
$ ps axu|grep grep
$ ps axu|grep grep
$ ps axu|grep grep
jidanni   1171  0.0  0.2  2376  608 pts/1    R    02:26   0:00 grep grep

Is it some kind of race condition?