My script has probably always worked but my graphical zip tool, Xarchiver (xarchiver.xfce.org), doesn't show its content :(

This is instead the output of console tool unzip:

unzip -l backup.zip 
Archive:  backup.zip
  Length      Date    Time    Name
---------  ---------- -----   ----
        1  2010-02-05 22:29   /home/user/a/a.txt
        1  2010-02-05 22:28   /home/user/b/b.txt
        1  2010-02-05 22:29   /home/user/c/c.txt
---------                     -------
        3                     3 files
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and your test script:

#! /usr/bin/perl
use strict;
use warnings;
use Archive::Zip qw( :ERROR_CODES :CONSTANTS );

my $zip = Archive::Zip->new('/home/user/d/backup.zip');
print $zip->memberNames();
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prints my backup.zip content as well:

perl test_script.pl
/home/user/a/a.txt/home/user/b/b.txt/home/user/c/c.txt
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Thank you very much for your answers :)