We present a study of dissipative structures for a class of the coupled kinetic-fluid models with partial relaxations at the linearized level. It is a generalization of several known results in the decoupled case that is either for the kinetic model or for the symmetric hyperbolic system. Precisely, a partially dissipative linearized system is of the type (p, q) if the real parts of all eigenvalues in terms of the frequency variable k admit an upper bound -lki 2 P /(1 + lkl 2 )q up to a common

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... ositive constant. It is well known that a symmetric hyperbolic system with partial relaxation is of the type (1, 1) if the so-called Shizuta-Kawashima conditions are satisfied. In the current study of the coupled kinetic-fluid models, we postulate more general conditions together with some concrete examples to include the case (1, 2) investigated also in [14] and the new case (2, 3). Thus, the coupled kinetic-fluid models may exhibit more complex dissipative structures.