>>literally "of nothing". like "'tis nothing".
>
>Interesting. Just as in Spanish ("de nada"). Although, the expression varies with region. "No hay de qué" is also quite common, something like "there is no (??? last word difficult to translate - no reason to thank, I guess).

And it gets weirder - our "nema na čemu" is literally, "has not on what". One needs to know two other phrases, "hvala na {~}" - thanks on (for) {~}, and "nema" - has not - to mean "there is none". So, "nema na čemu" actually means "there's nothing [to thank] for"... which is more or less what you just said :).