The CoDominium was an alliance between the United States and a re-established Soviet Union which imposed world peace. An interstellar drive was discovered which allowed colonies to be established by the CoDominium on planets around other stars. The time period the CoDominium existed is from about 2010 to its collapse in 2103.
Politically, the CoDominium was governed by the Grand Senate with elected senators from the US and USSR. The system was parliamentary in nature with the executive elected by the Senate from among its members. While there were political factions and cliques, there were no formal political parties.
The CoDominium also had various government departments such as the Bureau of Relocation and a military arm consisting of a space navy and marines.