Engineers may make various decisions based on the engineering judgment while they design a building, or may choose different methods for modeling the structural components, especially the way by which the deteriorating behavior of elements should be incorporated. Such decisions cause the engineering demand parameters (EDPs) to depend on the deterioration properties of a building considered in a seismic performance assessment. It is important to know how much those properties are going to be effective on or valuable for designing of low-rise asymmetric RC buildings, or how they affect the design decision makings. For the example buildings, the seismic performance is evaluated by performing the incremental dynamic analysis (IDA) and monitoring the lateral deformation versus the load-resisting capacities of the models. By introducing a new criterion, the influence of the deterioration properties on the seismic performance of models is then assessed, providing the results for both torsionally-stiff and torsionally-flexible models. Although the deterioration affects the torsionally-stiff models more rapidly than the torsionally-flexible types, its impacts depend on the value of hysteretic model parameters. In contrary to the torsionally-flexible models, the influence of deterioration on the torsionally-stiff buildings is sensitive to the building asymmetry. However, the variation of deterioration rate is very significant for the torsionally-flexible models. So, it is important to make careful design decisions for reducing the undesirable effects of the deterioration.