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Complementary Resistive Switches (CRS) alleviate size limitations for passive crossbar array memory devices by the elimination of sneak paths. Since CRS cells consist of two anti-serially connected bipolar resistive elements, e.g. electro-chemical metallization (ECM) elements, it is straightforward to use their corresponding memristive models for circuit simulation. Here we show that simple linear memristive models, which are often used in literature, are inapplicable. Therefore, we apply a physics based nonlinear model for ECM elements which is capable of simulating correct CRS behavior for anti-serially combined elements. Interconnecting memristive element models in CRS configuration is an advantageous way to check for memristive model consistency.