Original: Third parties, officially termed "nonparty political organizations" can appear on the ballot as well - five of these have had candidates on the ballot in Iowa since 2004 for various positions: the Constitution Party, the Iowa Green Party, the Libertarian Party, the Pirate Party, and the Socialist Workers Party.
Simplified: There are two major political parties in Iowa, the Iowa Democratic Party and the Republican Party of Iowa, as well as several unofficial third parties.