According to perlop, this is exactly what it does - it will keep going until the end before starting over. Thus, you want something like:

$rc = 1;
while (defined($nextfile = <$dirName/*cm*.4gl>))
{
  if ($rc) {
    $rc = system("grep $field $nextfile 1> /dev/null");
    if (!$rc) {
      print FOUND "$field $nextfile\n";
    }
  }
}
[download]

But I still don't like it. Use glob rather than the <> operator.

for my $nextfile (glob File::Spec->catfile($dirName, '*cm*.4gl')) {
  $rc = system("grep $field $nextfile 1> /dev/null");
  if (!$rc) {
    print FOUND "$field $nextfile\n";
    last;
  }
}
[download]

I'd also recommend a few minor other changes:

• Opening for reading: make it explicit with "<". open(FIELDS,"<fields.dat");. Also, use IO::File. But I just like the objects better.
• Your while can assign directly to $field: while (my $field = <FIELDS>). Don't use $_ if you're not using $_.
• Use the array version of system. To do this, you'll need a full path to grep, and you'll need to redirect STDOUT yourself. Arguably not worth the effort (it is a lot of effort if you want to use STDOUT elsewhere). But all it takes is getting bit merely once by a shell interpolation of something you didn't expect to make the benefits all too obvious.

Hope this helps.