When exporting records (including especially some fields from a related file), what does the order of available fields (left side of export-window) depend on?
I need them to be ordered alphabetically but they aren´t. The order doesn´t seem to reflect the current order in the related file, neither the order at the time when the relationship to the related file was created.

Not sure if this is what you're looking for [without actually launching FMP, etc.]; however, based on my experience, it would seem that the EXPORT ORDER of the fields is EQUAL TO the order in the "Define Fields" window. So, if you alphabetize your fields in the "Define Fields" window, that's the order in which they should export.

Note that this applies to version 6 and earlier. I have not yet exported records from 7, but I imagine they have not changed this.

Also, I'm not sure I've ever had to export fields from a related file - but maybe I have and never notice. I'm not sure what kind of relationship you're talking about or how you have things designed, but let me know if you continue to have difficulty and will check into this further, as a matter of curiosity.