Abstract Recently, we developed a model based on experimental data, which includes a pair of antagonistic muscles, a general load against which the muscles act, feedback pathways from muscle sense organs and spinal inhibitory circuits involving 1A interneurons and Renshaw cells. Descending inputs can activate the model through combinations of inputs to α-motoneurons, γ-motoneurons (via intrafusal muscles and their feedback pathways) or the 1A interneurons. The role of each of these connections is analysed here in terms of its effect on the response of the muscles to impulse inputs, with particular interest in the effects on the overall stability of the systems. Increasing muscle stiffness or feedback from muscle receptors tends to produce high frequency oscillations. Coactivation of α- and γ-motoneurons can lead to cancellation of oscillations, because of delays in the effects of γ-motoneurons on contraction. Connections of 1A inhibitory interneurons onto antagonist motoneurons accentuate the oscillations. Inhibitory connections from Renshaw cells onto α-motoneurons tend to prevent oscillations, whereas the concentrations onto γ-motoneurons may produce them.