Between February 1978 and February 1993, the average monthly unemployment rate for South Australia, Tasmania and Queensland was above that for the nation as a whole, while the average unemployment rate for Victoria and New South Wales was below the national figure. An important question is whether developments in Victoria which have beneficial effects on Victoria's unemployment problem also have long-term beneficial effects on the unemployment problems of its two high unemployment neighbours, Tasmania, and South Australia, and similarly for New South Wales and Queensland. If helpful spillovers do in fact occur, how significant are they? In particular, is it that Tasmania's and South Australia' s unemployment problems are mitigated more, in the long term by favourable developments in Victoria rather than by unemployment reducing developments which occur within their own borders and similarly for Queensland and New South Wales? The purpose of the paper is to investigate these and other related questions with-the help of a vector auto-regressive (VAR) model estimated from monthly data for the period-under consideration. The broad finding of the paper is that the "big-neighbour effect" on Tasmania, South Australia and Queensland is highly significant and ma y well outweigh the beneficial effects on unemployment of developments which are targeted at the three high unemployment states themselves or which occur accidentally within their borders.