The continuous complex wavelet transform offers a convenient framework for neural spike sorting. Results show that wavelet-based neural spike detection outperforms simple threshold detection, especially with signals with low signal to noise ratio. Classification of action potentials using their signatures in wavelet space performed as well as a classifier based upon principal components analysis, and better than a classifier based upon template matching. Applied on experimental intrafascicular recordings of muscle spindle afferent nerve response to passive muscle stretch, the spike sorting algorithm manages to isolate afferent activity of units having a linear relationship between neural firing rate and muscle length, an important step towards a model-based estimator of muscle length.