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#Maybe this what you mean????
open (F1, '<' ,$file1) or die "Cannot open file $file1 for reading\n";
open (F2, '<', $file2) or die "Cannot open file $file2 for reading\n";

while ( <F1>, <F2> )
{  
...

   # <F1> plays no role here - it is a No-Operation: NoOp
}

while ( <F2> ) 
{
  # $_ is a line from $file2
}