The approach depends on your requirements: if you want a robust script, then you may want to investigate parsers. However, if all you want is a quick hack; then you can think of it as a simple 2-state state machine: have you seen an "Fstrik yes" line since the previous string, or not.

  my $seen_Fstrik_yes = 0;
  while (<>)
  {
    if ($seen_Fstrik_yes && /<String '.*?'>)
    {
       $seen_Fstrik_yes = 0;
    }
    else
    {
      print;
      $seen_Fstrik_yes |= /<FStrik Yes>/;
    }
  }
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This method only works as a quick hack, and assumes a very specific format for its input. --Dave