Anarchists such as Proudhon, Bakunin, and Kropotkin advocate federalism. As far as I understood from their works, this entails an organizational structure in which power flows "upwards" and is expressed through agreements made by delegates at consecutively wider/higher levels.
The Wikipedia article on federalism mentions that this conception of federalism differs from what is normally understood when talking about federalism. It cites a passage from An Anarchist FAQ:
Since not all issues are local, the neighborhood and community assemblies will also elect mandated and re-callable delegates to the larger-scale units of self-government in order to address issues affecting larger areas, such as urban districts, the city or town as a whole, the county, the bio-region, and ultimately the entire planet. Thus the assemblies will confederate at several levels in order to develop and co-ordinate common policies to deal with common problems.
This sounds like council democracy, and doesn't look like it would differ significantly from "state federalism". I couldn't find a more detailed explanation of where exactly the difference lies between an anarchist and state interpretation of federalism, and would be grateful if someone here could provide that.