Variation on myocom's technique. Could be a little more elegant with IO::File:

use strict;
use warnings;

my ($input_file) = @ARGV;

# Auto-generate output names based on input name
my @output_file = map { "$input_file.$_" } 1..2; 

# Open up all the required filehandles
open($input_fh, "<", $input_file)
     || die "Could not open $input_file\n";

my @out_fh;

open ($out_fh[0], ">", $output_file[0])
     || die "Could not write to $output_file[0]\n";
open ($out_fh[1], ">", $output_file[1])
     || die "Could not write to $output_file[1]\n";

# Start by writing to the first filehandle
my $fh = $out_fh[0];

while (<$input_fh>)
{
      $fh = $out_fh[1] if (/^DETS01/);

      print $fh;
}

# Now close out everything
foreach my $out_fh (@out_fh)
{
      close($out_fh);
}

close($input_fh);
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This rotates filehandles if the string "DETS01" occurs. The first bit is in the first file, the second in the second. So the file "input.txt" makes "input.txt.1" and "input.txt.2".