I rode from Ljubljana to Zagreb today, 133km in 1:45hrs. Both these countries are in the EU and in the Schengen area but you still have to stop at the border and you get stamped out of Slovenia though this did not happen when I entered Slovenia from Austria or in any of the other Schengen countries, then the police check to see if you have a Vignette (Toll pass) stuck to your windscreen, lucky I had done this the day before, the Vignette is not valid if its not stuck to the screen. Then the Croatian guys stamped my passport as well but neither of them asked me to take my helmet off. So far no Customs has showed any interest in my bike or its paperwork. No tunnels on this ride you just have to go around the hills instead of through them, a lot more fun.
Unloaded and went walkabout, first impressions of the town are that its a bit time worn, in need of a coat of paint. The currency here is the Kuna not the Euro, population 793,000.