Unraveling complex interactions between animal species is of paramount importance to understand competition, facilitation, and community assembly processes. Using data from GPS positions of sheep (Ovis aries) and red deer (Cervus elaphus) grazing a moorland plot, we modeled the animal movement of each species as a function of the distance between individuals, with the aim to assess the role of animal interactions (i. e., attraction and repulsion) in their spatial movement. We used black box-based models. These models do not require making assumptions about the biological meaning of their parameters. They are data-driven and use embedding complex algorithms that create nonlinear functions that estimate the behavior of the system, in our case the movement of our animals, and its errors. We used an algorithm based on radial basis functions to build models of time series data, using minimum description length as the criteria for model optimization. Included in the model is a factor that captures the collective behavior of the animals based on the distance between individuals. The model emphasizes the spatial relationship between animals from the absolute navigational directions by attenuating the latter. Our simulations showed that animals of the same specie tend to group together, with sheep having a stronger grouping behavior than deer. The dynamics of the model are density dependent, that is, the number of animals within range affects the strength of the interactions and their grouping behavior. A strong swarm behavior was detected by the model, the longer the distance between species, the stronger the attraction between them; and the shorter the separation between species, the stronger their repulsion, which suggests inter- and intra-competition for food and space resources. Our modeling approach is useful to interpret animal movement interactions between animals of the same or different species, in order to unravel complex cooperative or competitive behaviors, or to make predictions of animal movement under different population scenarios. © 2012 Springer-Verlag and ISPA.