Inspired by Woodward’s account of causation and explanation, Caponi has recently defended that biology – and, especially, evolutionary biology – is grounded on a “mosaic of invariants”, that is, a net of causal regularities which, although not stable and universal enough to constitute genuine causal laws, may guarantee the explanatory autonomy of this discipline by supporting a certain number of relevant counterfactuals. In spite of lacking proper causal laws, evolutionary biology is a unitary theory because invariants are, in some sense, “subsumed” by other kinds of laws – the zero force laws, like the Hardy-Weinberg equilibrium, and the consequence laws, like the laws of population genetics –, which connect them within a more general theoretical framework. Might the explanatory structure of a hypothetical unified theory of cultural evolution be conceived in a similar way? The goal of the present project is to provide an answer to this question, by considering two related problems. Firstly, I shall attempt to identify the zero force laws and the consequence laws of the theory of cultural evolution. Secondly, I shall assess two case studies (namely, the rise and fall of empires and the evolution of technology), in order to determine if the causal regularities that are invoked in cultural evolutionary explanations may count as genuine invariants, in Woodward’s and Caponi’s sense.