Nebraska has a unique form of state government with only one legislative house. All members of this house hold the title of 'Senator.' The Legislature meets in the Nebraska State Capitol at Lincoln and is comprised of forty-nine members, each chosen by a single legislative district.  Senators are chosen for four-year terms, with one-half of the seats up for election every second year.  They are limited to two terms in office.

Rather than separate primaries held to choose Republican, Democratic, and other partisan contenders for a seat, Nebraska uses a single non-partisan primary election, in which the top two vote-getters are entitled to run in the general election rather like run-off voting elsewhere. There are no formal party alignments or groups within the Legislature, however they all 'lean' towards one party or another. The Democratic and the Republican parties do explicitly endorse candidates. The unofficial partisan makeup of the Nebraska Legislature is 31 Republicans, 15 Democrats, and 3 Independents. Currently, both Seantors representing Dawson County citizens are 'leaning' Republicans.

The above information from:  http://ballotpedia.org/wiki/index.php?title=Nebraska_House_of_Representatives
and: http://www.dkosopedia.com/wiki/Nebraska