There are a number of studies which consider the relation between military spending and economic growth using Granger causality techniques rather than a well-defined economic model. Some have used samples of groups of countries, finding no consistent results. Others have focused on case studies of individual countries, which has the advantage of the researchers bringing to bear much more data than the cross country samples and a greater knowledge of the structure of the economy and the budget. This paper adds to the literature by providing an analysis of two countries, Greece and Turkey, which are particularly interesting case studies given their high military burdens, the poor relations between the two and the resulting arms race in the area. In addition to analysing the data using standard "pre-cointegration" Granger causality techniques, this paper employs modern vector autoregressive (VAR) methodology that utilises cointegration via Granger's representation theorem. The standard Granger causality tests suggest a positive effect of changing military burden on growth for Greece, but this is not sustained when the cointegration between output and military burden is taken into account. The only evidence of significant Granger causality is a negative impact of military burden on growth in Turkey.