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Associated with the notion of the mixed L p -affine surface area for multiple convex bodies for all real p (p = −n) which was introduced by Ye, et al. [D. Ye, B. Zhu, J. Zhou, arXiv, 2013 (2013 , 38 pages], we define the concept of the mixed L p -dual affine surface area for multiple star bodies for all real p (p = −n) and establish its monotonicity inequalities and cyclic inequalities. Besides, the Brunn-Minkowski type inequalities of the mixed L p -dual affine surface area for multiple star bodies with two addition are also presented.doi:10.22436/jnsa.009.05.76 fatcat:ssgawwaj2zaezmvhndwebv7wgy