The ongoing Turkish-Greek antagonism has triggered the interest of defense economists to investigate the various aspects of the arms race between Turkey and Greece. However, empirical studies examining the long-run relationship between the military expenditures of the two countries offer little evidence in favor of such an interaction. This paper attributes the poor results of the previous literature to the adherence to linear cointegration techniques and argues that if the adjustment towards long-run equilibrium is asymmetric, nonlinear co-integration models should be employed. Accordingly, this paper considers threshold autoregressive (TAR) and momentum threshold autoregressive (M-TAR) models as alternative adjustment processes for the cointegration relationship, following Enders and Siklos (2001). The results indicate that the relationship between the variables can be characterized by a threshold cointegration specification following an M-TAR type adjustment process.