  Noncommutative gauge fields (similar to the type that arises in string theory
with background B-fields) are constructed for arbitrary nonabelian gauge groups
with the help of a map that relates ordinary nonabelian and noncommutative
gauge theories (Seiberg-Witten map). As in our previous work we employ
Kontsevich's formality and the concept of equivalent star products. As a
byproduct we obtain a ``Mini Seiberg-Witten map'' that explicitly relates
ordinary abelian and nonabelian gauge fields.
