My notebook is a Dell Inspiron 6000 with Windows XP Home - updated 
I have recently installed the avast! Home edition on my personal notebook. Until then I used the ZoneLabs firewall, but now I experience lots of errors, so I might consider to quit ZoneLabs.
Are there any compliant software firewalls or can anybody recommend some?
Hey renehfrederiksen. Wow that’s a mouthful. Read the Zone Labs Forums and you will see you have alot of company with problems using that Firewall. I had problems myself, but it was with the latest version of Sunbelt Kerio Firewall, and I had to uninstall it. I am currently using an old version of Kerio 4.2.2 downloaded from filehippo.com and it is working fine. It can be used in simple mode, but with a few minor setting changes, will detect a few more leak tests than ZA Free. (Not Pro) This for me is enough protection, but maybe your looking for more? In that case go to Comodo Firewall web site. I used the latest version, and liked it as it was very user friendly, but it was also a little bit too heavy on my system. This will be taken care of soon I have read, and I may go back to it. I’m sure the more experienced users will weigh in here as well, but I hope I have helped a little.
There are others, Jetico, Sunbelt Kerio, etc.
See some firewall tests for comparison, some are freeware but many are paid for versions http://www.firewallleaktester.com/tests.php. Also see http://www.thefreecountry.com/security/firewalls.shtml