Are Masters degrees from German universities of applied sciences (Fachhochschulen) eligible for PhD? Are Masters degrees from German universities of applied sciences (Fachhochschulen) eligible for PhD?

If I do a Masters in any of the German universities of applied sciences (Fachhochschulen), would I be able to apply for a PhD in any other Universities/research institutes in Germany?
The basic answer is "Yes, but. . . ."

A master's degree is usually the minimum prerequisite for admission to PhD programs in Germany. However, many faculties within various German universities have established "qualification" procedures for degrees they do not believe to be "equivalent" to their own. This usually includes some combination of coursework (with the associated exams), plus evaluation of the master's thesis to show equivalency to the expected degree. 

These criteria are often applied not only to international students, but to students from German Fachhochschule as well. However, these policies vary widely between universities, and between different departments at the same universities, so you should contact the specific programs you're interested for more details.