grep - argument list too long

I am trying to use grep/egrep to find a file in the /tmp directory. All I get back is ~# grep -R "a1aaaa" /tmp/* -bash: /usr/bin/grep: Argument list too long Admittedly, there are numerous files in /tmp, how do I get around this limitation in grep? for a in /tmp/*; do grep "a1aaaa" $a; done seems to work for one directory only, but I feel this method to be clumsy as it does not give me recursion into subdirectories. Any way to do it directly with grep/egrep? Peter