Regimental Sergeant Major (RSM) is an appointment held by Warrant Officers Class 1 in the British Army and Royal Marines. The RSM is the senior warrant officer in a regiment or battalion, and is primarily responsible for maintaining standards and discipline. In the Household Cavalry he is the Regimental Corporal Major (RCM).
The RSM is never addressed as "Sergeant Major". He is addressed as "Mr (surname)" by officers, and as "Sir" or "Mr (surname), Sir" by his inferiors. Only his commanding officer (the lieutenant colonel commanding his battalion or regiment) has the privilege of addressing him as "RSM".
The same appointment exists in the Australian Army, New Zealand Army and Singapore Armed Forces. In the Canadian Armed Forces, RSMs now hold the rank of Chief Warrant Officer.
The equivalent rank in the US Army would be a Command Sergeant Major.