In spite of many years of research there is still much uncertainty regarding the nature of proprioceptive signals and the role of these signals in kinaesthesia and movement control. The uncertainty mainly concerns the firing characteristics of the most numerous proprioceptors, the muscle spindles. From many studies in anaesthetized animals it is known that mammalian muscle spindle afferents respond to muscle displacement and velocity and that these responses are strongly modulated by ã_fusimotor activity emanating from the central nervous system. Fusimotor action not only increases the firing rate of spindle afferents at a given muscle length ('bias'), it also controls the sensitivity of the afferents to changes in muscle length ('gain'). Just how the mammalian nervous system controls fusimotor action in daily life remains the subject of controversy (for review, see Prochazka, 1996). The firing rate of muscle spindles can also be affected by mechanical factors such as tendon strain, changes in pennation angle, Journal of Physiology (1998) 1. The aim of this work was to compare the ability of several mathematical models to predict the firing characteristics of muscle spindle primary afferents recorded chronically during normal stepping in cats. 2. Ensemble firing profiles of nine hamstring spindle primary (presumed group Ia) afferents were compiled from stored data from 132 step cycles. Three sets of profiles corresponding to slow, medium and fast steps were generated by averaging groups of step cycles aligned to peak muscle length in each cycle. 3. Five models obtained from the literature were compared. Each of these models was used to predict the spindle firing profiles from the averaged muscle length signals. The models were also used in the reverse direction, namely to predict muscle length from the firing profiles. A sixth model incorporating some key aspects of the other models was also included in the comparisons. 4. Five of the models predicted spindle firing well, with root mean square (r.m.s.) errors lower than 14% of the modulation depth of the target profiles. The key variable in achieving good predictions was muscle velocity, the best fits being obtained with power-law functions of velocity, with an exponent of 0·5 or 0·6 (i.e. spindle firing rate is approximately proportional to the square root of muscle velocity). The fits were slightly improved by adding small components of EMG signal to mimic fusimotor action linked to muscle activation. The modest relative size of EMG-linked fusimotor action may be related to the fact that hamstring muscles are not strongly recruited in stepping. 5. Length was predicted very accurately from firing profiles with the inverse of the above models, indicating that the nervous system could in principle process spindle firing in a relatively simple way to give accurate information on muscle length. 6. The responses of the models to standard ramp-and-hold displacements at 10 mm s¢ were also studied (i.e. velocities that were an order of magnitude lower than that during ...