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The paper gives the systematic characterization of eigenspace in max-T algebra where T is equal to ukasiewicz t-norm. Max-ukasiewicz fuzzy algebra can be used for the description of the states of Discrete-event systems. The states can represent a balance of the resource unit expended during the evolution of the system (for example fuel or money). In the contribution, the classification of max-ukasiewicz eigenspaces is described and explained by the two-dimensional examples-in this case it is possible to accompany the example with illustrative graphs. However the description of the eigenspace for the higher dimensions is also outlined.