Unique effects of the double helical conductances of the surfaces (HCS) on the Mueller matrix (Mm) of a two-layer eccentrically bianisotropic cylinder linear array are investigated in this paper. The mathematical treatment is conducted based on the boundary-value approach combined with the technique of generalized separation variables. Both the TMz- and TEz-polarization of the obliquely incident waves are taken into account in the analysis. To gain insight into some physical mechanisms, numerical examples are presented to show the influences of the variations of the twist angles on the behavior of Mm of a linear array of four bianisotropic cylinders. Correspondingly, various magnetic symmetry groups (such as D∞(C∞), C∞v(C∞), D∞h(D∞), C∞h(C∞)) and some generalized symmetry and anti-symmetry relations, which govern all the elements of Mm or the scattering cross section under special chiral operations, are demonstrated. The present studies can be exploited to identify the constitutive characteristics of some bianisotropic media and to provide better understanding of the electromagnetic wave interaction with bianisotropic cylindrical objects with complex boundaries.