When the brain interacts with the environment it constantly adapts by representing the environment in a form that is called an internal model. The neurobiological basis for internal models is provided by the connectivity and the dynamical properties of neurons. Thus, the interactions between neural tissues and external devices provide a fundamental means for investigating the connectivity and dynamical properties of neural populations. We developed this idea, suggested in the 1980s by Valentino Braitenberg, for investigating and representing the dynamical behavior of neuronal populations in the brainstem of the lamprey. The brainstem was maintained in vitro and connected in a closed loop with two types of artificial device: (a) a simulated dynamical system and (b) a small mobile robot. In both cases, the device was controlled by recorded extracellular signals and its output was translated into electrical stimuli delivered to the neural system. The goal of the first study was to estimate the dynamical dimension of neural preparation in a single-input/single-output configuration. The dynamical dimension is the number of state variables that together with the applied input determine the output of a system. The results indicate that while this neural system has significant dynamical properties, its effective complexity, as established by the dynamical dimension, is rather moderate. In the second study, we considered a more specific situation, in which the same portion of the nervous system controls a robotic device in a two-input/two-output configuration. We fitted the input-output data from the neuro-robotic preparation to neural network models having different internal dynamics and we observed the generalization error of each model. Consistent with the first study, this second experiment showed that a simple recurrent dynamical model was able to capture the behavior of the hybrid system. This experimental and computational framework provides the means for investigating neural plasticity and internal representations in the context of brain-machine interfaces.