Thanks! It's clear now :) I added alarm_remove() to remove the old alarms

Working code:

#!/usr/bin/perl

use strict;
use warnings;

use POE;

use Time::HiRes qw(time);

POE::Session->create
  ( inline_states =>
      { _start => sub {
            $_[KERNEL]->alias_set('timer');
            $_[KERNEL]->post('timer', 'wakeup');
        },

        wakeup => sub {
            print "wakeup at ", scalar localtime(), "\n";
            $_[KERNEL]->alarm_remove( $_[HEAP]{wakeup_alarm_id} ) if $
+_[HEAP]{wakeup_alarm_id};
            $_[HEAP]{wakeup_alarm_id} = $_[KERNEL]->alarm_add( wakeup 
+=> int( time() ) + 2 );
            $_[HEAP]{wokeup_alarm_id} = $_[KERNEL]->alarm_add( wokeup 
+=> int( time() ) + 2 );
        },

        wokeup => sub {
            $_[KERNEL]->alarm_remove( $_[HEAP]{wokeup_alarm_id} ) if $
+_[HEAP]{wokeup_alarm_id};
            print "wokeup at ", scalar localtime(), "\n";
        },
      },
  );

POE::Kernel->run();
exit 0;
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