If you want use $oFile = undef as a done flag, test to see if the @FileList entry equals undef before processing:

foreach $oFile(@FileList) {
   next unless defined $oFile;
   if ($oFTP->put("p:/charts/Sendtray/$oFile")) {
      if (move("p:/charts/Sendtray/$oFile","p:/charts/Sendtray/G
+ONE/$oFile")) {
          &LogSentFiles($oFile);
          $oFile = undef;
       }
   }
}
[download]

A cleaner way of representing your set of files is with a hash:

foreach (keys %Dir) {
   $FileSet{$_}++ 
       unless $_ eq "." || $_ eq ".." || $_ eq "GONE" || $_ eq "";
}
[download]

Then as the files are moved, you may delete them from the hash.

-Mark