Non-coordinated monetary policy is analysed in a stochastic two-country general equilibrium model. Non-coordinated equilibria are compared in two cases: one where policy is set in terms of state-contingent money supply rules and one where policy is set in terms of state-contingent nominal interest rate rules. In general the non-coordinated equilibrium differs between the two types of policy rule but a number of special cases are identified where the equilibria are identical. The endogenous choice of policy instrument is analysed and the Nash equilibrium in the choice of policy instrument is shown to depend on the interest elasticity of money demand.