Professorship without PhD in the United States In the discussion made in comments to this question, it has been stated that in France, it is possible (though improbable) to become a professor without having PhD. It made me curious if there is such possibility in the United States. I know that in 1970s there were leading professors in the US university who had only MSc. However, I think the main focus was on knowledge in the past, but now formalities are much more important.

Anyway, I am curious if the current regulations in the US universities allows this at all? For promotion to full professor, one needs to be assistant/associate professor. In the past, having a PhD was privilege, but it is now mandatory for holding any assistant/associate/full professor.

Does the current regulations allow a professor without PhD to teach PhD students?

This question is about impossibility vs. improbability.
At most US institutions, you need the terminal degree in your field. For many fields this is a PhD, but in some it might be an EdD, a DMA, a DPH, a ThD, etc. However, all of these degrees are considered to one level or another to be research doctorates. Presumably faculty positions at a medical school require an MD or equivalent. Likewise for other professional schools. Positions in the visual arts, theater, dance, creative writing, cinematography, etc., may only require the MFA (Master of Fine Arts) degree, as it is considered to be the terminal degree in those fields. 

"Regulations" about the requirements to hold certain academic ranks and perform certain academic duties (like mentor graduate students) are made at the institutional level.