Probably a Dipodascus species.

I forgot to mention that I have even wondered whether perhaps this is no ascomycete, greeting, Ida

Sorry I did not see that there is a reply.Thanks I am going to investigate this,
Ida

I went through the descriptions of the species of this genus in Mycobank. It seems that my specimen is close to D. armillaria, australiensis and D. geniculatus, but differs from these and all other species (of which descriptions were available) in the large asci: 44-80 x 16-24 um and the larger spores: 8-10.5 x 3,5 -6 um.
From the description I learned that those things that I had considered a imperfect parasite are indeed the anamorf, and that my specimens produces plenty of arthrospores and a few chlamydospores.
All description on Mycobank are from cultures and I wonder whether the size of asci and spores can be different in cultures from in nature. Does anyone know?
Ida

The size of the asci is iindeed quite variable. An accurate identification will not be possiible wiithout a pure culture. You will find the necessary information in Studies in Mycology vol. 29 and vol. 50: 489-515, 2004. Freely available for download.

Thanks a lot for the literature. As far as I can see it could be either D. aggregatus or D. australiensis.
It differs, however, from both in the much larger number of spores 100 (estimated) versus 20-30/ ascus, the wider asci (16-24 µm versus 6-11) and  the narrower spores (Q 2.0-2.8 versus ca. 1.2-1.3 and ca. 1.5-1.6).