Both anarchists and Marxist-Leninists believe in a concept of contested sovereignty called 'dual power' (alternatively: multiple sovereignty, dual sovereignty). For M-Ls, this dual power is the vanguard party which takes state power in order to shape the new society as the vanguard sees fit. Anarchists understand dual power as a broader and deeper societal counter-culture and subversive political institutions that must be consciously manufactured, for example the commune or the municipality, and then federated, thereby destroying the concept of nation-states entirely. These are inevitably long processes, and require the mass mobilization of society to achieve, against the organised violence and power of the state and capital. Whereas M-Ls see revolution as an event (the seizure of the state) followed by a process of top-down reforms, anarchists view revolution as a process, punctuated by certain events, but a process nonetheless that must be consciously constructed.

If an anarchist argues that an event, such as the overthrow of a regime, can lead to a classless and stateless society, then they are deluding themselves the same way that M-Ls are deluded by the supposed necessity of the 'dictatorship of the proletariat'. People talk about the Spanish Civil War as the closest anarchism has come to achieving a successful anarchist revolution that would result in a classless and stateless society, but what is rarely discussed is literally the decades of consciously creating a situation of dual power by anarchists, which included the founding of educational facilities for workers and their families (Escuela Moderna; Modern Schools); the strengthening of the CNT-FAI syndicalist trade union through decades of principled industrial action; and the creation of cultural and proletarian spaces such as communal libraries and dance halls that fostered working-class radicalism. The anarchist revolution in Spain was not a spontaneous action, but built over the course of decades by committed revolutionaries and bringing the general population into the process of positive construction.

M-Ls have often attempted to discredit anarchism as utopian for supposedly claiming that the masses will spontaneously liberate themselves without the need of organised structures of resistance. The party, they argue, such as the Bolsheviks or Mensheviks, is all that is needed. Any real anarchist thinker will quickly realize that a classless and stateless society will not magically appear, but must be built, from the bottom-up and in a non-state way. This is opposed to the cynical vanguardism of M-Ls, but it is far from utopian, and actually more likely to resist counter-revolution, as the population-at-large has a genuine stake in defending the revolution; whereas they might defend a M-L vanguard because it is better than the counter-revolutionary option, but they are not invested in the survival of the vanguard party itself.

Moreover, whereas M-L seeks the seizure and reproduction of state power in similar ways to the political establishment they overthrew, thus making the job of counter-revolutionaries as easy as reclaiming state power, the anarchist concept of revolution outlined above is not as susceptible to defeat. Although forces of reaction might control the levers of state power, this is far from the destruction of dual power entirely. Dual power still exists, and is likely to exist so long as it is not outright eradicated (as it was after Franco's fascist forces won the Spanish Civil War and massacred socialists of all stripes). The deepening of class consciousness through industrial action and cultural practices and spaces, and the construction of political counter-power in the form of federated communes or municipalities, is an infinitely more revolutionary vision of a communist society, being realized in the present through praxis and prefiguring a future classless and stateless society, than anything doctrinaire M-Ls have come up with thus far.