That seems odd. What's your OS and version of Perl? On my RH9 default install of Perl

#!/usr/bin/perl
($dev,$ino,$mode,$nlink,$uid,$gid,$rdev,$size,$atime,$mtime,$ctime,$bl
+ksize,$blocks)=stat("/tmp/foo.txt");

print localtime($atime) . "\n";
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Returns the last accessed time and does not count as a file access.

Does your script do anything else with these files?