Amsterdam has a city-wide council responsible for crime prevention, education etc, and 15 borough councils which deal with more mundane matters like garbage collection and community groups.
www.amsterdam.nl Official council website. The english button takes you back to the wretched I amsterdam website again.
The city council (gemeente) is "governed" by a non-elected mayor (Job Cohen) and aldermen. The mayor is technically a crown appointee. People who have served a few years in parliament and then quit often get nice mayoral jobs in the provinces. Being mayor of Amsterdam is considered a plum job. There has been talk of moving to a system of mayoral elections for years, but nothing ever comes of it.
The councillors themselves are elected every four years. All official Amsterdam residents have a vote.
The city council is made up of the following parties:
PvdA (Labour) 15
VVD (Free-market Liberals) 9
GroenLinks (Green, leftwing) 6
CDA (Christian Democrats) 4
SP (Socialist party) 4
D66 (Reformist social democrats) 3
Leefbaar Amsterdam (Liveable Amsterdam, loony local party) 2
Amsterdam Anders / De Groenen (Left-wing locals,old provos) 1
Mokum Mobiel (Pro car lobby) 1