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The phrase
Herr Doktor Professor
is relatively well-known amongst non-German speaking English-speakers. But assuming that all three words are used, what order is it in? Is it Herr/Frau Doktor Professor (what I assumed was the case, as it progresses from the most common to the least common honorific), or Herr/Frau Professor Doktor, as mentioned in Is writing "Herr Prof. X" exaggerated/mandatory? Is it old-fashioned??
Both Professor and Doktor are titles much like the historical Freiherr. Titles are added to the name in descending order, the highest ranking title first. Therefore, Professor must be placed before Doktor.
Herr Professor Doktor Liebig …
However, it is rather uncommon to use both titles except in door signs and maybe the salutation of formal letters. Usually one would restrict oneself to one title in German.
Herr Professor Liebig …
Note that for these intents and purposes, Herr and Frau do not count as titles. (Titles need to be gained but every grown-up is automatically either Herr or Frau; neither of them were ever explicitly gained. This was likely different two centuries ago.)
To answer that question properly, one has to consider that Doktor is a academic grade, while Professor is an official title compareable to General or Bundeskanzler. This plays an important role not only inside Universities, where old traditions still regulate how two Professors have to approach each other, but also for daily use: To handle the so called "Professorenproblem", the Munich University recommends, to write Professor in an extra line, separated from name and title, when adressing a letter.
Herrn Professor
Dr. Dr. h.c. mult. Claus-Wilhelm Canaris
Adress
This is a contradiciton to DIN 5008, whish recommends to write Herr. Prof. Dr. Faustus. According to Munich Universitiy these two styles of adressing an professor allow for a separation between academics and non-academics.
In any case, the more honorable appelation Professor should be written before Doktor or Dr.
In oral communication, as well as in the appelation line of a letter, the Professor scores off the Doktor, so it is ok, to simply say "Herr Professor" without mentioning the Doktor.
As the title Professor is related to an employment as a Professor, special rules apply for retiered people. In most cases they may keep the title, but some institutions demand them to denominate themselfes Emeritus or Prof. Emer.
