How did you set up your paragraph style?
Are you using a TAB STOP to define the bullet indent? Or are you using INDENTS to define the bullet indent?
I suspect the former is the case.
You need to set up hanging indents where the bullet Left Indent is positive and the First Line Indent is negative.
Here is a screenshot example:
MT.Freelance, thanks for your answer.
At the moment I left the second lines of my lists as they are, no tab stops or other.
I tought there muste be a "better" solution than +/- indent lines. It sounds a little bit not-so-cool :-)
For one-line-only items, a simple indent is sufficient. However, for items longer than one line, as in your example where the bullet or number at the beginning of the line needs to align with the start of the item above it, and the wrapped-around line must align with the text of the item that begins after the number or bullet, you need to define the paragraph style to do that. A negative first-line indent and a positive rest-of-lines indent is the standard way to do this in all applications that can set type, not only InDesign. It's called a hanging indent.
Search Google for "hanging indent" or "InDesign hanging indent" without quotes for lots of info like this: