1. The ultrastructure of all the afferent fibres, or all the efferent fibres, was studied in selected nerves from chronically de-afferentated or de-efferentated cat hind limbs perfusion-fixed with glutaraldehyde.2. The following parameters were measured: number of lamellae in the myelin sheath (n), axon perimeter (s), external fibre perimeter (S), axon cross-sectional area (A). Fibres were allocated to afferent groups I, II, III or efferent groups alpha and gamma according to the number of lamellae in the myelin sheath.3. The thickness of the myelin sheath (m) was linearly related to axon perimeter within the range s = 4 mum to s = 20 mum (groups II, III and gamma). The relation m = 0.103 s - 0.26 provided a good fit for all afferent and efferent axons in this range in several different anatomical muscle nerves in three cats. The myelin sheaths were thinner in a fourth, presumably younger, cat.4. The myelin sheaths were relatively thinner for large fibres in groups I and alpha (s = 20-50 mum). The results are interpreted in one of three ways. Either m tends to a limit of about 2.2 mum, or m is linearly related to s such that for large fibres m = 0.032 s + 1.11.5. Alternatively, m may be considered to be proportional to log(10)s for all sizes of axon so that m = 2.58 log(10) S - 1.73. The interpretation that there are two separate linear relations for large and small fibres is favoured.6. The ratio of axon to external fibre perimeter (g) falls from about 0.70 for group III and small gamma fibres in the cat to about 0.62 for group II and large gamma fibres and then rises again to 0.70, or even 0.75 for group I and alpha axons.7. The above relations between m and s are combined with the observations of Boyd & Kalu (1979) that Theta = 5.7 D for groups I and alpha and Theta = 4.6 D for groups II, III and gamma. It is shown that Theta = 2.5 s approximately for all sizes of axon (s from material fixed for electron microscopy) in rat, cat and man. The accuracy of this equation may be improved by deducting 3 m/sec in the case of small fibres. This conclusion is compatible with experimental observations of the relation between l and D (Hursh, 1939; Lubinska, 1960; Coppin, 1973) and between l and Theta (Coppin & Jack, 1972).8. From the theoretical analyses of Rushton (1951) and others Theta should be proportional to the external dimensions of the fibre rather than to axon size. It is shown that the thinning of the myelin sheath ought to affect Theta substantially. Thus some other factors must compensate for the thinning of the sheath.9. Small fibres are significantly more non-circular than large fibres. From the quantitative data of Arbuthnott et al. (1980) it is concluded that non-circularity may contribute to the fact that Theta proportional, variant s rather than Theta proportional, variant S, but cannot wholly account for it. Other possibilities considered are that axoplasmic resistivity or specific nodal conductance may differ for large and small fibres.10. It is suggested that myelinated peripheral nerve fibres may fall into two distinct classes with different properties, one comprising groups I and alpha and the other groups II, III and gamma. The conclusion predicted from theory may apply to each of these classes separately so that Theta = 2.0 S for the large-fibre class and Theta = 1.6 S for the small-fibre class.