Multiple-scattering LIDAR return calculations obtained by seven different models for the same specified numerical experiment are compared. This work results from an international joint effort stimulated by the workshop group called MUSCLE for MUltiple SCattering Lidar Experiments. The models include approximations to the radiative-transfer theory, Monte-Carlo calculations, a stochastic model of the process of multiple scattering, and an extension of Mie theory for particles illuminated by direct and scattered light. The model solutions are similar in form but differ by up to a factor of 5 in the strength of the multiple-scattering contributions. Various reasons for the observed differences are explored and their practical significance is discussed.