Abstract. An analysis is given of dispersion in an optical fibre waveguide having a continuous radial variation of refractive index using the scalar wave approximation. Solutions are presented for the particular case of Selfoc fibre taking into account mode dispersion, material dispersion and group delay. It is shown that for a correctly matched input Gaussian beam the pulse dispersion is small although in practice it is likely to be ∼ 1 ns over a length of 1 km.