State governments in the United States have almost identical structural models as the federal system, with three branches of government:  executive,  legislative, and  judicial. State governments are integral to the country’s workings because the Tenth Amendment to the United States Constitution accords all governmental powers not granted to the federal government's reserved for the states.¹ State governments in a federal country share sovereignty with the federal governments.
The legislative branch of states are comprised of state legislatures. 49 out of the 50 states, with the exception of Nebraska have a bicameral legislature. The upper house is the Senate and the lower house is the House of Representatives.¹ The head of the executive branch of every state is an elected Governor. Most executives in the US have several key members who are also elected and each state is allowed to organize this branch however they choose.¹ The judicial branch of many states ends at a state supreme court. The structure of courts is also at the discretion of each individual state.¹
The 50 states of the US
Most states are divided into counties or something equivalent, who although have some governmental authority, are accorded no sovereignty. These divisions vary hugely between states. Although there are absolute federal powers, tasks such as law enforcement, education, health, transportation and infrastructure are considered state responsibilities and initiatives.
1. State Government. Retrieved from http://www.usa.gov/Agencies/State-and-Territories.shtml
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