Ok, first, to clear something up. Just like a movement can claim to be socialist while keeping all the capitalist modes of production while also negating basic freedoms to its citizens - so too can a movement be socialist without claiming that or using its traditional symbolism or lexicon… However, in EZLN and Rojava case - both do that.

Rojava

The main ideological leader behind Kurdish resistance in Turkey and its successful revolution in Syria is Abdullah Ocalan. He is the founder of the PKK, Kurdistan’s Workers Party, and has lead a guerilla war in the name of the Kurdish State, absolute gender equality and against capitalism from 1970s until his arrest in 1999. He has since been imprisoned for life in Turkey. However, while being a Marxist Leninist in the beginning, he changed his mind, and the whole ideology of his party, towards more Anarchist Socialism by releasing several books that are the foundation of his ideology of “democratic federalism”, which is in most ways just an evolved version of Anarcho-syndicalist ideology as implemented in Spain.

Here are some words from the big man himself:

"The PKK, while proving Kurdish existence beyond any doubt, got stuck in nation-statism. The ensuing period of self-criticism revealed the anti-socialist and anti-democratic essence of nation-statism. The speedy dissolution of real socialism in the 1990s contributed to a deeper understanding of the underlying factors behind the crisis. The dissolution of real socialism was caused by power and real socialist nation state problematics. To be more precise, the crisis of socialism was the result of an inadequate understanding of the problem of power and the state. When the contradictions of state and power, set out so starkly by the Kurdish question, coalesced with the wider global crisis of real socialism, a comprehensive analysis of the issue of the state and power became inevitable. To this end, in a significant part of my defense, I tried to analyze the state and power throughout civilizational history. I concentrated on presenting the transformation of the phenomena of state and power in the context of capitalist modernity – the present-day hegemonic civilization. I specifically argued that the transformation of power into the nation-state was the basis of capitalism. This was an important thesis. I tried to demonstrate that in the absence of power being or gained through the nation-state model, capitalism could not have become the new hegemonic system. The nation-state was the fundamental tool that made capitalist hegemony possible. Therefore, I tried to prove that socialism, as anti-capitalism, presenting itself as what I call ‘historical-society’, could not establish itself as based on the same state model, in other words, as a real socialist nation-state. I tried to show that the idea that socialism, as proposed by Marx and Engels, could only be constructed through central nation-states was indeed a fundamental defect of scientific socialism. I went on to present 10the thesis that socialism could not be constructed through the state, especially the nation-state, and that an insistence on this could only result in the most degenerate versions of capitalism as experienced in many instances, but especially in the actually existing socialism of Russia and China. As a necessary precur- sor to this thesis, I analyzed the system of central civilization throughout history, the concept of power, and the structure of capitalist modernity’s state and power which is the prevalent structure unique to our era. My main conclusion was that socialists could not have a nation-state principle. Rather, the solution to the national question should be based on the principle of the democratic nation. The practical expression of this, as I will try to show, is the KCK (Union of Democratic Communities in Kurdistan) experience.” -

Democratic Nation - by Abdullah Ocalan

I would gather that this makes it very clear that the ideology of Democratic Federalism, as implemented in Rojava, is no doubt socialism. In it, worker-cooperatives (not for profit ones) are prevalent and use of the lands in its many communes is often common. It is a true attempt at a stateless, ecological, feminist and just society where the workers own the means of production. I will not bombard you with links to interviews, on-the-ground reporting, books and other products of the Rojava revolution. You are clearly well read and can use the internet, and can easily find snippets from daily life troubled but free Rojava.

EZLN

EZLN, admirably, refrains from putting an exact title to its political orientation, simply putting it as “left”, they are very clearly an Anarchist/Socialist society. They have a functioning demonetized, cooperative economy, free healthcare and education and, to be frank, this is the freaking flag. I think it is statement enough.