You might try something like this:

foreach (@lines) {
   next unless /start-phrase-here/ .. /stop-phrase-here/;

   # process
}
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If you have no 'stop' phrase, you might use 'undef' on that side of the .. operator, or go with a more logical-looking flag approach:

my $flag;
foreach (@lines) {
   $flag++ if /start-phrase/;
   next unless $flag;

   # process
}
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U: I can't believe I didn't mention this originally, but you should probably be aware that parsing any HTML on your own is going to be extremely hard/unreliable, unless you have precise control over the formatting of the page. Better to use an HTML::Parser-derived module to pull the HTML data into Perl, and then work with the Perl data structure to get what you need.