Broad-band dielectric spectroscopy (10(-1)-10(7) Hz) has been used to study the molecular dynamics in a set of bisphenol A poly(ester carbonate)s (BPA-PECs) and tetramethylbisphenol A poly(ester carbonate)s (TMBPA-PECs) containing 1,4-cyclohexylene dicarboxylate (CHDC) linkages. Four dielectric relaxation processes are observed: The dynamic glass transition (a-relaxation) being characterized by a Williams-Landel-Ferry (WLF-behavior) temperature dependence. Additionally three secondary relaxations (beta-, gamma'-, and gamma*-relaxation) exist. The beta -relaxation is related to the flip-flop motion of the cyclohexylene rings and becomes dielectrically active because of a coupling to the neighboring carbonyl units. The gamma'- and gamma*-relaxations originate from fluctuations of the carbonyl groups as well, either by their own librational motions or by a coupling to the flips of the adjacent phenylene groups. Replacing the hydrogen atoms in the phenylene rings ortho to the carbonate units (BPA-PEC) by methyl groups (TMBPA-PEC) alters drastically the molecular dynamics below and above the calorimetric glass transition.