Ocular fixation test and ocular fixation index (OFI) never have been interpreted in terms of mathematical models, despite their widespread diffusion. However, ocular fixation is a typical case of visual-vestibular interaction, and mathematical models have proven very helpful in interpreting some mechanisms of this interaction, e.g. those of the optokinetic-vestibular interaction. In the present paper, a first attempt is proposed toward a model interpretation of OFI. By using very simple mathematical models, the hypothesis is tested that visual suppression of vestibular nystagmus results from direct action of smooth pursuit system (SPS). The aim is to draw consequences and recognize possible limits of this hypothesis. Dependence of OFI on SPS performance is examined. Although the available experimental data are insufficient for comprehensive validation of the model, the results agree with the current interpretations. In particular, quantitative support is given to the sensitivity of OFI to central vestibular diseases. Although the interpretation of visual suppression and OFI in terms of mathematical models is still at a very preliminary stage, models may provide a theoretical reference framework for the interpretation of new experimental results and/or suggest new test protocols.