This paper describes methods for second-order stereology of spatial fibre systems. For stationary and isotropic fibre processes it gives practicable estimators of the K-function and the pair correlation function, which are based on planar sections. The second-order methods are applied in transmission electron microscopy analysis of blood capillaries in the rat thyroid. They lead to the result that the capillaries show an inhibitory pattern of their spatial arrangement, with a hard-core distance of about 2.6 microm. There is a close relationship to three-dimensional size characteristics estimated recently for these elliptical capillaries.