The axon determines whether or not it is myelinated by the Schwann cell. At maturity there is a positive correlation between sheath thickness and axon calibre. This correlation is initially very low or absent, but gradually strengthens during development. This:increase could come about because the axon continuously controls Schwann cell myelinating activity, so that a given axon calibre is associated with a particular myelin sheath thickness, an interaction which would entail the Schwann cell continuously monitoring and responding to axon size. This seems unnecessarily complex. This theoretical study shows that the strong correlation between the 2 parameters within a given myelinated fibre population may come about in a much simpler way than outlined above. This is demonstrated by modelling the growth and myelination of a hypothetical population, utilising data from earlier studies on cervical ventral motoneuron axon development. The hypothesis tested shows that the only instructive interactions by the axon on the Schwann cell necessary for the strong correlation between the 2 parameters to emerge are for the initiation of myelination, its continuation and its termination. These: could result fi om a single stimulus being switched on, persisting for a time and being switched off Under this influence, the Schwann cell is assumed to proceed to form the myelin sheath at a constant rate which it itself inherently determines, in the absence of any quantitative influence exerted by the axon. This continues until the stimulus for myelination ceases to emanate from the axon. The validity of the hypothesis is demonstrated, because the resulting myelin-axon relationships correspond closely to those observed during development.