Problem with 2 local domains

[eluser]Justin Question[/eluser]
Hello,
let me first say, that I like CodeIgniter very much. It's light, not hard to understand and almost properly working :-)

Now to my problem,
I developed a single site 'DomainA' and everything was runnning fine on my localhost with MAMP as server. Then I copied the domain folder including CodeIgniter to build a second site under htdocs/DomainB and set the base_url in config.php to 'DomainB'. I changed some pages to see the difference to DomainA.

So far, no problem, the browser shows the correct homepage of each domain.
When I click on a link of the homepage, the browser loads the next page from the domains folder.
But..
as soon as I click a second time on a DomainB page, it loads a page from DomainA. This is true for all links, the first time it loads correctly, the second time it switches to the other domain.

What is happening here? Thank you for helping.