An eruptive fluctuation is defined operationally as an increase in numbers over at least two generations, followed by a marked decline. Reported eruptions in ungulates suggest that the upswing is initiated by a change in food or habitat and is terminated by overgrazing. An apparent exception–the Kaibab eruption–probably also fits this pattern. The interpretation causally linking reduction of predators on the plateau with increase of deer is an overstatement of evidence. Eruption of established populations is essentially the same process as the buildup of populations initiated by liberation, with the difference that in the second case a zone of high density migrates radially from the point of liberation. Eruption of thar (a goat—like bovid) after liberation in New Zealand was studied by sampling populations at different distances from the point of liberation. The aim was to determine trend of demographic statistics across an eruptive fluctuation that spans 50 years. Although fecundity varied across the eruption, the major influence on rate of increase was traced to variation in death rate. The major component of this variation was the rate of mortality over the first year of life. Trend in death rate, and hence in rate of increase, was associated with trends in other population statistics that are easier to measure. The most useful correlative of rate of increase is probably the level of fat reserves. While we do not know whether trends in population statistics of thar reflect those of other ungulates during an eruptive fluctuation, the generality of the reported trends may usefully serve as a testable hypothesis.