[Yves wrote]: Thank you very much for this hint - I actually need a
test that returns true if all children carry the attribute AND if there are element children at all [...]

there are always many ways of phrasing these things. [...]

for example to write the xpath to match the english above you could write

(every $c in * satisfies $c[@attribute]) and *

although a more compact way to say that in english is to say no child
 exists which does not have the attribute, or in xpath

not(*[not(@attribute)])