Third order (primary) aberration theory has had little application to the design of aspheric spectacle lenses. Such an application would be useful because: 1. Third order theory is useful in designing simple optical systems, as relatively simple equations can be used to obtain approximate magnitudes of aberrations and to show how these aberrations change with variations in design parameters without recourse to a large mass of data. 2. Aspherising one or both surfaces of spectacle lenses allows the correction of off-axis power errors in high positive power lenses where this would be otherwise impossible, and enables other factors, such as distortion correction, to be considered simultaneously with off-axis power error correction over the total range of lens powers. Third order formulae are developed for calculation of distortion in thin spectacle lenses, when one or both surfaces are conicoid aspherics. Results are presented which show the validity of using third order theory. Solutions which allow correction of rotatory or peripheral distortion, when one lens surface is a conicoid aspheric, are illustrated. A study of these solutions shows that one of the off-axis power errors (eg. oblique astigmatism) and one of the distortions can be simultaneously eliminated, but the lens forms required are too curved to be cosmetically feasible.