A conservation-law-based approximation for the mean waiting times in priority service systems with a mixture of exhaustive, gated, one-limited service strategies and star polling sequence is presented. The authors generalize previous results presented by Manfield (1985) for a similar system with one-limited service at the low-priority stations. For service systems with one-limited stations the proposed approximation is a low or medium traffic approximation. However, for systems with a mixture of gated and exhaustive services the approximation is very accurate for the whole range of admissible traffic intensities.>