which u s states do not have a bicameral legislature 
all states in the u s but one are bicameral with both a house and a senate the one exception is nebraska which has just a one chamber legislature the bottom linea bicameral legislature refers to a style of government with a two house legislative system in the u s congress has two houses the house of representatives and the senate as such it s a bicameral legislature this system can be contrasted with the unicameral system in which all members of a legislature deliberate and vote as a single group 