This work makes use of a biomechanical model of speech production as a reference subject to address several phenomena related to the adaptability and stability of speech motor control, namely motor equivalence and postural stability. The first part of this thesis is related to the phenomenon of motor equivalence. Motor equivalence is a key feature of speech motor control, since speakers must constantly adapt to various phonetic contexts and speaking conditions. The Uncontrolled Manifold (UCM) idea offers a theoretical framework for considering motor equivalence in which coordination among motor control variables is separated into two subspaces, one in which changes in control variables modify the output and another one in which these changes do not influence the output.This concept is developed and investigated for speech production using a 2D biomechanical model. First, a representation of the linearized UCM based on orthogonal projection matrices is proposed. The UCMs of various vocal tract configurations of the 10 French oral vowels are then characterized using their command perturbation responses. It is then investigated whether each phonetic class such as phonemes, front/back vowels, rounded/un-rounded vowels can be characterized by a unique UCM, or whether the UCMs vary significantly across representatives of these different classes. It was found that linearized UCMs, especially those that are specifically computed for each configuration, but also across many of the phonetic classes allow for a command perturbation response that is effective. This suggests that similar motor equivalence strategies can be implemented within each of these classes and that UCMs provide a valid characterization of an equivalence strategy. Further work is suggested to elaborate which classes might be used in practice.The second part addresses the question of the degree to which postural control of the tongue is accomplished through passive mechanisms - such as the mechanical and elastic properties of the tongue itself - or through short-latency reflexes - such as the stretch reflex.A specific external force perturbation, was applied to the 2D biomechanical model , namely one in which the tongue is pulled anteriorly using specific force profile exerted on the tongue body using a force effector attached to the superior part of the tongue blade. Simulation results were compared to experimental data collected at Gipsa-lab under similar conditions.This perturbation was simulated with various values of the model's parameter modulating the reflex strength (feedback gain). The results showed that a perturbation rebound seen in simulated data is due to a reflex mechanism. Since a compatible rebound is seen in data from human subjects, this can be taken as evidence of a reflex mechanism being involved in postural stability of the tongue. The time course of the mechanisms of this reflex, including the generation of force and the movement of the tongue, were analyzed and it was determined that the precision of the model was insufficient to make any conclusions on the origin of this reflex (whether cortical or brainstem). Still, numerous experimental directions are proposed.