We analize two different mechanical models for the Brownian Motion. The first model is composed of a hard disk (the colloidal particle) immersed in a gas of smaller and lighter hard disks. The second model is the same except for the particle shape that are squares. The basic difference in these two systems lies in the inter-particle interactions (elastic hard-core collisions): in the first case one has chaos, while the second system is non-chaotic. This difference does not reflect on the transport properties of the two systems. The numerical results for diffusion coefficient, correlation function and response function of the colloidal particle, both for the chaotic and non-chaotic systems, are in perfect agreement with kinetic theory. For the relaxation of fluctuations far from equilibrim instead one observes a dependence on the presence (or absence) of chaos.