The Alliance counted on the collaboration of the Jura Federation — created in November 1871 and directed by James Guillaume and Adhémar Schwitzguébel - in which he succeeded in advancing his "apolitical" theses, contrary to participation in elections and in "bourgeois" institutions.

Supporters of political intervention, following the theses approved at the proposal of Karl Marx at the Congresses of the International Workingmen's Association (IWA), formed the Geneva Federation.

According to the historian Josep Termes: "surely, this Alliance was born in order to achieve - through this coherent and secret group - that the Barcelona Workers' Congress, which would be held two months later, would come out decisively for collectivist anarchism and apoliticism, putting an end to the predominance of the societal, cooperative and politicist currents".

[3] To avoid being condemned at the IWA Conference that was to be held in London in mid-September 1871,[4] the Geneva Alliance decided to dissolve the previous month against opinion Bakunin himself, who was absent when the decision was made.

However, as Josep Termes has pointed out, the group continued to function as such even though the bureaucratic organization had disappeared, "since it was impossible for ideological and personal ties to stop influencing its conduct.

The delegates in favor of the "anti-authoritarian" positions signed a manifesto showing their disagreement with the expulsion and decided to meet in Saint-Imier, to hold a separate congress in which the expulsion of Bakunin and Guillaume was annulled, did not recognize the General Council appointed in The Hague and approved a resolution that included the anarchist theses, insisting that "the destruction of all political power is the first duty of the proletariat" and that "all allegedly provisional and revolutionary political power [... ] cannot be more than a hoax.

[...] It recognizes that all the existing political and authoritarian states, more and more reducing their activities to simple administrative functions of public service in their respective countries, will have to dissolve into a universal union of free associations, like the agricultural and industrial ones.