[1] In 1983, Nelson was elected to his first term as a council member representing what was then district 4 in Phoenix.
As vice-mayor, Nelson assumed the position and duties of mayor for a short period between March 17 and March 28 of that year, until the council had selected an interim replacement in councilwoman Thelda Williams.
In 2000, however, he resigned his position in order to run for a seat in the state House of Representatives, winning his election and beginning his first term in the legislature in 2001 representing district 17.
Following a redistricting, Nelson went on to win election in District 12 in 2002, where he and fellow representative Jerry Weires (as Arizona legislative districts are represented by 2 members) won reelection in 2004 and ran unopposed in 2006.
In 2008, Nelson successfully ran for the Arizona Senate in District 12.