An extended analysis of a vehicle following at close headway is carried out. A largely linear model of a vehicle is used to permit the computation of a large convoy. Vehicular interactions within a convoy in which each vehicle receives only information on the status of the preceding vehicle are analysed and a matrix representation of the set of interactions is developed, the main emphasis being on the propagation of spacing errors within the convoy. The conditions for positive impulse response, attenuation of error and stable, non-oscillatory response are identified in terms of both pole placement and volume space in which stable operating conditions may be located. The implications of the choice of controller parameters are studied with four examples and related to the information flow strategy and requirements within each convoy. The paper then presents the proposed short headway controller design methodology.