Initial European reactions to President Reagan's Strategic DefenseInitiative (SDI) speech were a mixture of disbelief and irritation. European military-strategic concerns are several and are presented in the paper in five separate butoverlapping sections: 1) questions about coupling, the credibility of theAmerican nuclear guarantee and effects on NATO strategy and doctrine; 2) concerns about strategic instabilities and the arms race; 3) worries about the future of arms control and the ABM Treaty; 4) speculation about the impact on the French and British nuclear forces and alliance cohesion; and 5) anxieties over the enormous costs involved.