In a recent study, the Two-Layer Crossing Channels Micromixer (TLCCM) exhibited good mixing capacities in the case of the Newtonian fluids (close to 100%) for all considered Reynolds number values. However, since the majority of the used fluids in the industrial sectors are non-Newtonians, this work details the mixing evolution of power-law fluids in the considered geometry. In this paper, the power-law index ranges from 0.73 to 1 and the generalized Reynolds number is bounded between 0.1 and 50. The conservation equations of momentum, mass and species transport are numerically solved using a CFD code, considering the species transport model. The flow structure at the cross-sectional planes of our micromixer was studied using the dynamic systems theory. The evolutions of the intensity, also the axial, radial and tangential velocity profiles were examined for different values of the Reynolds number and the power-law index. Besides, the pressure drop of the power-law fluids under different Reynolds number was calculated and represented. Furthermore, the mixing efficiency is evaluated by the computation of the mixing index (MI), based on the standard deviation of the mass fraction in different cross-sections. In such geometry, a perfect mixing is achieved with MI closed to 99.47 %, at very small Reynolds number (from the value 0.1) whatever the power-law index and generalized Reynolds numbers taken in this investigation. Consequently, the targeted channel presents a useful tool for pertinent mass transfer improvements, it is highly recommended to include it in various microfluidic systems. 5939 the case of creeping flows (Re of the order of 0.1). Temporary perturbation concerns twodimensional flows where solid boundaries and/or initial conditions are disturbed over time.Regarding the spatial perturbation, it makes the geometry twisted in the three directions of space. These perturbations break the flow regularity and so the chaotic flow is generated. For this subject, it became necessary to focus the efforts on the development of micromixers used in the different industrial domains such as bioengineering and chemical engineering, chemical synthesis, emulsion processes, polymerization [1], DNA analysis, two-phase flow separation [2], detection and analysis of chemical or biochemical content [3-4-5]. We can distinguish two main types of micromixers: active and passive micro-mixers [6]. Active micromixers use external energy sources to accentuate the flow agitation by, for example, a magnetic field, pressure field, and electrical field, etc. These types of micromixers are very efficient in terms of mixing [7] but they are more complex and expensive than passive micromixers. In addition, they required more detailed in terms of fabrication. Besides, passive micromixers are of great importance due to their simple structures and easy manufacturing [8]. Thus, the secondary flows resulting from the chaotic advection are very intense and many vortices of different sizes are generated. The large vortices improve the macroscopi...