In the context of our current planetary crises, in a world that continues to be shaped by capitalist, colonialist, androcentric and anthropocentric visions, we are faced with the urgency of reconsidering, at the deepest levels, the way we relate with other human and nonhuman beings. This working paper aims to contribute towards that end by looking at human-nonhuman relations through the concept of conviviality, understood as the everyday living together with difference, and how it intersects with inequality. In the first part of this paper, more-than-human conviviality-inequality is investigated by critically analyzing onto-epistemological and methodological approaches that question, subvert or reproduce hegemonic thinking and worldviews on humannonhuman relations like historical materialism, new materialisms, transhumanism, posthumanisms, and indigenous relational ontologies. In the second part, I look at particular relational dimensions like incompleteness, translation, and affect, which can help us create new understandings of more-than-human conviviality-inequality in Latin America and beyond.