Hello Guido
In moodle 2.3 there is a setting "prevent late submission' if set to 'Yes' prevent students from submitting assignment. But in moodle 2.4 and 2.5 you need to set 'Cut off date' to prevent students from submiiting late work. If you set some cut off date that means the assignment will not accept submissions after this date without an extension. And due date means "this is when the assignment is due. Submissions will still be allowed after this date but any assignments submitted after this date are marked as late. To prevent submissions after a certain date - set the assignment cut off date."