Thanks for your answer, I did actually found the problem myself, it was just that.
But then I ran into another, more serious problem. I have a number of custom post types, defined through Custom Post Type UI as suggested. All the settings seemed just fine, specific users set as Author to specific post types. Looking at the user's roles I could it seemed that the user had all the rights I wished. But no user, not even the site wide editor having the same rights as me (administrator) regarding all post types, could publish any new posts. Because this was very critical, I had to uninstall the plugin.
For now I just use the standard WP user groups. It's not that I don't trust my users, I just wanted to simplify things for them. Users that are a bit unsecure of what to do, and afraid to "destroy the whole site", tend to be more comfortable if they don't have more options than they should. I'm sure this plugin can do this for me, once I get all the settings right…