The characteristics of a thermally forced connected-vessel thermosyphon operating in an oscillatory mode have been determined using analytical techniques, the outcome of which is compared with results obtained by numerical integration of the governing equations. From a previous investigation it was known that adequate phase-plane representations of the limit cycles associated with oscillations could be obtained if the vessel-volume ratio was sufficiently small. This study aims at demonstrating how this constraint on the vessel volumes can be relaxed by prescribing a Mandelstam condition, that is, by postulating that the total heat content of the system remains conserved during the rapid phases of the oscillation. It was concluded that incorporating this Mandelstam condition in the analysis had the highly beneficial consequence that good analytical results could be obtained for much larger values of the vessel-volume ratio than those previously permitted.