In the paper fibre processes are considered, i.e. discrete sets of curves distributed at random in the plane. For translation invariant fibre processes the PALM distribution of the angle in a typical fibre point is defined, and point processes are studied which are obtained by intersection with lines. As a special case motion invariant, i.e. translation invariant and isotropic, fibre processes are treated. Finally weighted fibre processes are considered. As example segment processes are investigated.