Use a sort sub-routine. Don't know how you want to sort (you give no example :), but here's a start:

# sample data
my @filenames = '20001212_20011212_text.asp',
                '20021212_20031212_text.asp',
                '20031212_20041212_image.asp',
                '20011212_20021212_image.asp');

# loop
for (sort { sort_me(); } @filenames) {
  # whatever
  print "$_\n";
}

sub sort_me {

  # grab info from special vars $a and $b
  my ($a_date1,$a_date2) = split '_', $a;
  my ($b_date1,$b_date2) = split '_', $b;

  # then do your sort - eg, to sort by date1 then date2
  # (in the date format I have used above)
  ($a_date1 <=> $b_date1)
  ||
  ($a_date2 <=> $b_date2);
}
[download]

$a and $b are special vars used within a sort. Read this for more info.

Note, this is a rough demo - not gonna test it unless you supply actual data and comparisons... but should give you an idea where to start.

cLive ;-)

Update - just realised you don't need to know type, so have amended code accordingly. later one, removed semi-colon that didn't affect outcome, but still looked out of place...